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Magnetic Force - Definition, Formula, Magnetic Force on a Current-Carrying Conductor, FAQs

Magnetic Force - Definition, Formula, Magnetic Force on a Current-Carrying Conductor, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 04:52 PM IST

The magnetic force is an outcome of the electromagnetic force. This magnetic force is caused by the movement of charged particles. The magnetic force is a force that is produced by magnetic field interactions. In this article, we will discuss what is magnetic force, the magnetic force formula, features of interaction between electric field and magnetic field, right hand thumb rule, Coulomb's law for magnetic force, magnetic force on a current-carrying conductor class 12, magnetic force examples, and moving charges and magnetism formulas.

This Story also Contains
  1. What is Magnetic Force
  2. Magnetic Force Formula
  3. Features of Interaction Between Electric Field and Magnetic Field
  4. Coulomb's Law for Magnetic Force
  5. Magnetic Force on a Current-Carrying Conductor Class 12
  6. Magnetic Force Examples
  7. Moving Charges and Magnetism Formulas
Magnetic Force - Definition, Formula, Magnetic Force on a Current-Carrying Conductor, FAQs
Magnetic Force - Definition, Formula, Magnetic Force on a Current-Carrying Conductor, FAQs

What is Magnetic Force

Consider a point charge ‘q’ placed in both magnetic and electric fields. The magnitude of the magnetic field is given by B and the magnitude of the electric field is given by 4E. The total force on the charge q is given as the summation of both electric and magnetic force that acts on the charge i.e. FE+FM, where FE is the electric force and FM is the magnetic force.

The definition of magnetic force can be written as:

The magnetic force is the force of attraction or repulsion that acts between two accelerated charged particles which are exerted on one charge by the magnetic field produced by the other charged particle.

Magnetic Force Formula

The value of the magnitude of the magnetic force relies on the amount of charge that is in motion and the distance between them. The mathematical expression of the magnetic force can be written as,

F=q[E(r)+v×B(r)]

where,

  • F is the total force acting on the charged particle
  • q charge of the particle
  • E(r) is the electric field vector at position r
  • v is the velocity vector of the particle
  • B(r) is the magnetic field vector at position r

This magnetic force is known as the ‘Lorentz Force’. It describes the force which is known as the combined electric and magnetic force of a point charge q which is caused due to EM fields.

Features of Interaction Between Electric Field and Magnetic Field

The features of the interaction of Electric and Magnetic fields are discussed below:

  • The magnetic force is a dependent quantity. It depends on the charge q of the accelerated particle, velocity v of the particle, and magnetic field B.
  • The magnetic force direction is opposite to the direction of the positive charge i.e. in the direction of the negative charge.
  • The cross product or vector representation of the velocity v of the particle and the magnetic field B gives the magnitude of the magnetic force in the vector form. Also, the cross product can be replaced with sinθand the expression is written as F=qvBsinθ, where θ denotes the angle between the velocity component and the magnetic field component. And this θ is found to be less than 180 degrees.
  • The resultant force stands normal to the velocity and magnetic field direction. The direction of the magnetic field is calculated by the right-hand thumbs rule or right-hand slap rule.
  • The total magnetic force becomes zero for static charges, that is, the magnetic force is found only in moving charges. Also, the magnetic force of the charged particle moving in a parallel direction to the magnetic field is zero.
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Right-Hand Thumb Rule

If the current-flowing conductor is held by the right hand, the direction facing the thumb gives the direction of the flow of electric current and the direction of other curled fingers gives the direction of the magnetic field carried by the current-carrying conductor.

Coulomb's Law for Magnetic Force

Coulomb's law for magnetic force tells that the magnetic force between any two poles in a magnetic medium should have direct proportionality with their pole strength and inversely proportional to the absolute permeability and the square of the distance between the two poles. The mathematical expression for this law is given as

Fm1m2μ0r2F=km1m2μ0r2

Where

  • m1 and m2 stands for their pole strength
  • r is the distance between the poles,
  • μ0 is the absolute permeability
  • k is the constant proportionality.

Magnetic Force on a Current-Carrying Conductor Class 12

The resultant force stands normal to the velocity and magnetic field direction. The direction of the magnetic field is calculated by the right hand thumbs rule.

The magnetic force will be produced by the magnetic field in a straight long current-carrying conductor. Consider the length of the conductor to be l and the area of the cross-section to be A. Let the n number density of the electrons. When the conductor is placed in some external magnetic field B,

Magnetic force on a moving charge:

F=qv×B

The current in the conductor will be given as

I=nqvdA

Where

  • n is charge carrier density
  • q is the charge
  • vd is the drift velocity
  • A is the cross-sectional area

The force for a small length dl of the conductor is

dF=q(vd×B)nAdl

The magnitude of the magnetic force due to a current-carrying conductor is

F=ILBsinθ

Magnetic Force Examples

  1. Aurora Borealis, the northern lights is an example of magnetic force in moving charges.
  2. Magnetic levitation trains are an example of magnetic force on a current-carrying conductor.
  3. The compass needle is an example of magnetic force on magnetic materials.
  4. Magnetic force is used in Cyclotron and mass spectrometers.
  5. Loudspeakers and electric bells are the everyday applications of magnetic forces.

Moving Charges and Magnetism Formulas

The important topics and their formulas related to the concept of moving charges and magnetism are given in the table below:

ConceptFormula
Lorentz ForceF=q(E+v×B)
Magnetic Force on a Moving ChargeF=q(v×B)
Magnetic Force on a Current-Carrying ConductorF=IL×B
Magnitude of Magnetic ForceF=qvBsinθ
Magnetic Field of a Long Straight Current-Carrying WireB=μ0I2πr
Magnetic Field at the Center of a Circular LoopB=μ0I2R
Ampere’s Circuital LawBdl=μ0Ienc
Biot-Savart LawdB=μ04πIdl×r^r2
Force Between Two Parallel Current-Carrying WiresF=μ0I1I2L2πr
Cyclotron Radiusr=mvqB
Cyclotron Time PeriodT=2πmqB
Magnetic Moment of a Current LoopM=IA
Torque on a Current Loopτ=M×B
Potential Energy of a Magnetic DipoleU=MB

Also read:

Frequently Asked Questions (FAQs)

1. What is a magnetic force or give the magnetic force definition:

The magnetic force is the force of attraction or repulsion that acts between two accelerated charged particles which are exerted on one charge by the magnetic field produced by the other charged particle.

2. Give some magnetic force examples:

Some of the components that work with the help of the magnetic force are a compass, MRI scanner, speaker, electric motor, computer and so on.

3. What is the magnetic force formula or write down the mathematical expression for magnetic force:

The cross product or vector representation of the velocity v of the particle and the magnetic field B gives the magnitude of the magnetic force is given in the vector form and the relation is F=q[v✖B]. Also, the cross product can be replaced with sinθ and the expression is written as  F=qvBsinθ, where θ denotes the angle between the velocity component and the magnetic field component. And this θ is found to be less than 180 degrees.

4. Is the magnetic field a scalar quantity?

The magnetic field is not a scalar quantity. As it contains both magnitude and direction of its own, the magnetic field is defined to be a vector quantity.

5. What is the law of magnetic force?

Coulomb's law for magnetic force tells that the magnetic force between any two poles in a magnetic medium should have direct proportionality with their pole strength and inversely proportional to the absolute permeability and the square of the distance between the two poles. Mathematical expression for this law is given as 

6. What is magnetic force?
Magnetic force is the attraction or repulsion exerted by magnetic fields on moving charged particles, current-carrying conductors, or other magnets. It is a fundamental force in nature that plays a crucial role in various electromagnetic phenomena and technologies.
7. How is magnetic force different from electric force?
While both are electromagnetic forces, magnetic force acts on moving charges or current-carrying conductors, whereas electric force acts on stationary charges. Magnetic force is always perpendicular to the motion of the charge or current, while electric force can act in any direction relative to the charge.
8. Why does a current-carrying wire experience a force in a magnetic field?
A current-carrying wire experiences a force in a magnetic field because current is the flow of moving charged particles. Since magnetic force acts on moving charges, each charge carrier in the wire experiences a force, resulting in a net force on the entire wire.
9. What is the right-hand rule for determining the direction of force on a current-carrying conductor?
The right-hand rule for a current-carrying conductor states: point your thumb in the direction of the current, your fingers in the direction of the magnetic field, and your palm will face the direction of the force on the conductor.
10. What happens to the magnetic force on a current-carrying wire if the current direction is reversed?
If the current direction in a wire is reversed, the direction of the magnetic force on the wire will also reverse. This is because the force depends on the direction of current flow, as indicated by the right-hand rule.
11. What is the formula for magnetic force on a moving charged particle?
The magnetic force (F) on a charged particle moving in a magnetic field is given by F = qvB sin θ, where q is the charge of the particle, v is its velocity, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field lines.
12. Why does a stationary charged particle experience no magnetic force?
A stationary charged particle experiences no magnetic force because magnetic force only acts on moving charges. The formula F = qvB sin θ shows that when velocity (v) is zero, the magnetic force (F) becomes zero, regardless of the charge or magnetic field strength.
13. How does the strength of a magnetic field affect the force on a moving charged particle?
The strength of the magnetic field (B) is directly proportional to the magnetic force (F) on a moving charged particle, as shown in the equation F = qvB sin θ. Doubling the magnetic field strength will double the magnetic force, assuming all other factors remain constant.
14. What is the formula for magnetic force on a current-carrying conductor?
The magnetic force (F) on a current-carrying conductor in a magnetic field is given by F = ILB sin θ, where I is the current in the conductor, L is the length of the conductor in the magnetic field, B is the magnetic field strength, and θ is the angle between the current direction and the magnetic field lines.
15. What determines the direction of magnetic force on a moving charged particle?
The direction of magnetic force on a moving charged particle is determined by the right-hand rule: point your thumb in the direction of the particle's velocity, your fingers in the direction of the magnetic field, and your palm will face the direction of the force for a positive charge (reverse for negative charge).
16. How does the magnetic force on a current-carrying loop differ from that on a straight wire?
A current-carrying loop experiences a net torque in a uniform magnetic field, causing it to rotate, while a straight wire experiences a net force causing it to move. This difference arises because the forces on opposite sides of the loop are in opposite directions, creating a rotational effect.
17. How does changing the shape of a current-carrying conductor affect the magnetic force it experiences?
Changing the shape of a current-carrying conductor can affect the magnetic force it experiences by altering the effective length and orientation of the conductor in the magnetic field. For example, a coiled wire may experience a different net force compared to a straight wire with the same total length.
18. What is the Hall effect, and how is it related to magnetic force?
The Hall effect is the production of a voltage difference across an electrical conductor when a magnetic field is applied perpendicular to the flow of current. It's related to magnetic force because the force on moving charges in the conductor causes charge separation, resulting in the Hall voltage.
19. How does the mass of a charged particle affect its motion in a magnetic field?
The mass of a charged particle doesn't affect the magnitude of the magnetic force it experiences, but it does affect its motion. Heavier particles will have a larger radius of curvature when moving perpendicular to a magnetic field, while lighter particles will have a smaller radius of curvature.
20. What is magnetic flux, and how is it related to magnetic force?
Magnetic flux is a measure of the total magnetic field passing through a given area. While it doesn't directly determine magnetic force, changes in magnetic flux can induce electric currents (Faraday's law), which can then experience magnetic forces.
21. What is the difference between diamagnetic, paramagnetic, and ferromagnetic materials in terms of their interaction with magnetic fields?
Diamagnetic materials weakly repel magnetic fields, paramagnetic materials are weakly attracted to magnetic fields, and ferromagnetic materials are strongly attracted to magnetic fields and can retain magnetization. These differences arise from how their electron configurations interact with external magnetic fields.
22. How does temperature affect the magnetic properties of materials?
Temperature can significantly affect the magnetic properties of materials. For ferromagnetic materials, increasing temperature reduces their magnetization, eventually leading to a complete loss of magnetic properties above the Curie temperature. For paramagnetic materials, increasing temperature typically decreases their magnetic susceptibility.
23. What is the principle behind magnetic resonance imaging (MRI), and how does it relate to magnetic forces?
MRI uses strong magnetic fields and radio waves to create detailed images of the body. The magnetic field aligns the spin of hydrogen nuclei in the body. Radio waves then cause these nuclei to resonate and emit signals. While MRI doesn't directly use magnetic forces, the interaction between the magnetic field and the nuclear spins is fundamental to the technique.
24. How do magnetic forces contribute to the formation and structure of galaxies?
Magnetic forces play a significant role in galaxy formation and structure. Large-scale magnetic fields in galaxies can influence gas dynamics, star formation, and the propagation of cosmic rays. These magnetic forces can help shape galactic structures like spiral arms and contribute to the overall stability of the galactic disk.
25. How do magnetic forces affect the behavior of superconductors?
In superconductors, magnetic forces play a crucial role in the Meissner effect, where the material expels magnetic fields below its critical temperature. This is due to supercurrents induced in the material that create opposing magnetic fields. In type II superconductors, magnetic forces also contribute to the formation of quantized magnetic flux vortices.
26. What is magnetic reconnection, and how does it relate to magnetic forces?
Magnetic reconnection is a process where magnetic field lines break and reconnect, releasing stored magnetic energy as kinetic energy and heat. This process involves complex interactions of magnetic forces as the field lines reconfigure. Magnetic reconnection is important in phenomena like solar flares, magnetospheric substorms, and fusion plasma behavior.
27. How do magnetic forces affect the behavior of neutron stars and magnetars?
Neutron stars and magnetars have incredibly strong magnetic fields that exert enormous forces. These magnetic forces affect the star's structure, cooling rate, and emission properties. In magnetars, the extreme magnetic forces can cause "starquakes" and powerful gamma-ray flares. The magnetic fields also influence the surrounding space, affecting particle acceleration and radiation processes.
28. How do magnetic forces contribute to the formation and behavior of accretion disks around compact objects?
In accretion disks around compact objects like black holes or neutron stars, magnetic forces play a crucial role. They can drive turbulence, which enhances angular momentum transport in the disk. Magnetic forces also contribute to the launching of jets and winds from the disk. The interaction between the disk's rotation and magnetic fields can lead to complex dynamics and energy release.
29. What is the concept of magnetic helicity, and how does it relate to magnetic force?
Magnetic helicity is a measure of the twist and linkage of magnetic field lines in a volume. While not directly a force, it's related to the stored energy in magnetic fields and can influence how magnetic forces evolve in a system. Conservation of magnetic helicity can constrain the behavior of magnetic fields in plasmas, affecting phenomena like solar eruptions and dynamo processes.
30. How does the angle between a current-carrying wire and magnetic field lines affect the force?
The angle (θ) between the current-carrying wire and magnetic field lines affects the force according to the sin θ term in the equation F = ILB sin θ. The force is maximum when the wire is perpendicular to the field (θ = 90°, sin 90° = 1) and zero when it's parallel (θ = 0° or 180°, sin 0° = sin 180° = 0).
31. How does the length of a current-carrying conductor affect the magnetic force it experiences?
The length (L) of the current-carrying conductor is directly proportional to the magnetic force (F) it experiences, as shown in the equation F = ILB sin θ. Doubling the length of the conductor in the magnetic field will double the force, assuming all other factors remain constant.
32. What is the principle behind the operation of an electric motor?
An electric motor operates on the principle of magnetic force on a current-carrying conductor. It consists of a current-carrying coil placed in a magnetic field. The magnetic force causes the coil to rotate, converting electrical energy into mechanical energy.
33. How does the concept of magnetic force apply to the Earth's magnetic field?
The Earth's magnetic field exerts forces on moving charged particles, such as those in the solar wind. This interaction creates phenomena like the auroras and helps protect the Earth from harmful solar radiation by deflecting charged particles.
34. What is the Lorentz force, and how does it relate to magnetic force?
The Lorentz force is the combination of electric and magnetic forces on a point charge due to electromagnetic fields. The magnetic component of the Lorentz force is identical to the magnetic force we've discussed (F = qvB sin θ). The complete Lorentz force equation is F = q(E + v × B), where E is the electric field.
35. How do magnetic forces contribute to the formation of cosmic jets from black holes?
Magnetic forces play a crucial role in the formation of cosmic jets from black holes. The intense magnetic fields around rotating black holes can channel plasma along field lines, accelerating it to near-light speeds. These magnetic forces help collimate the plasma into narrow, powerful jets that can extend for thousands of light-years.
36. What is magnetic levitation, and how does it work?
Magnetic levitation is the suspension of an object using magnetic fields to counteract gravitational force. It works by creating a strong magnetic field that repels the magnetic field of the levitated object. This can be achieved using electromagnets or superconductors, which exhibit perfect diamagnetism below their critical temperature.
37. How do magnetic forces contribute to the operation of a mass spectrometer?
In a mass spectrometer, magnetic forces are used to separate ions based on their mass-to-charge ratio. Ions are accelerated and then passed through a magnetic field. The magnetic force causes the ions to travel in circular paths, with the radius of the path depending on the ion's mass and charge. This allows for the separation and identification of different ions.
38. What is the cyclotron frequency, and how is it related to magnetic force?
The cyclotron frequency is the frequency at which a charged particle rotates in a uniform magnetic field. It's given by f = qB/(2πm), where q is the charge, B is the magnetic field strength, and m is the particle's mass. This frequency is directly related to the magnetic force, which causes the circular motion of the particle.
39. How do magnetic forces affect the behavior of plasma in fusion reactors?
In fusion reactors, magnetic forces are used to confine and control the hot plasma. Strong magnetic fields exert forces on the charged particles in the plasma, keeping them away from the reactor walls and maintaining the high temperatures and densities needed for fusion. This magnetic confinement is crucial for achieving sustained fusion reactions.
40. How do magnetic forces contribute to the formation and behavior of solar prominences?
Solar prominences are large, loop-like structures of plasma on the Sun's surface, shaped and held in place by magnetic forces. The Sun's complex magnetic fields exert forces on the charged particles in the plasma, guiding their motion and creating these dramatic structures. Changes in these magnetic forces can lead to solar flares and coronal mass ejections.
41. What is the concept of magnetic pressure, and how does it relate to magnetic force?
Magnetic pressure is the pressure exerted by a magnetic field on a plasma or conductor. It's related to magnetic force in that it represents the force per unit area exerted by the magnetic field. The magnetic pressure is proportional to the square of the magnetic field strength (B^2/2μ₀, where μ₀ is the permeability of free space).
42. How do magnetic forces affect the motion of charged particles in the Van Allen radiation belts?
The Van Allen radiation belts are regions of charged particles trapped by Earth's magnetic field. Magnetic forces cause these particles to spiral along magnetic field lines, bouncing back and forth between the Earth's magnetic poles. This complex motion, guided by magnetic forces, creates the distinctive shape and behavior of the radiation belts.
43. What is the Hall thruster, and how does it use magnetic forces for spacecraft propulsion?
A Hall thruster is a type of electric propulsion device used in spacecraft. It uses magnetic and electric fields to ionize and accelerate a propellant (usually xenon). The magnetic field traps electrons, which then ionize the propellant. The electric field then accelerates the ions, producing thrust. The magnetic force plays a crucial role in confining the electrons and creating an efficient ionization region.
44. What is the principle behind magnetic bottle confinement, and how does it relate to magnetic force?
A magnetic bottle is a configuration of magnetic fields used to confine plasma. It works by creating stronger magnetic fields at the ends of a cylindrical region, which exert forces on charged particles, reflecting them back towards the center. This confinement relies on the magnetic force's dependence on field strength and particle velocity.
45. How do magnetic forces contribute to the acceleration of cosmic rays?
Magnetic forces play a crucial role in cosmic ray acceleration. In processes like diffusive shock acceleration, charged particles gain energy by repeatedly crossing shock fronts, guided by magnetic fields. The magnetic forces cause the particles to spiral along field lines and scatter off magnetic irregularities, allowing them to gain enormous energies over time.
46. What is the concept of magnetic tension, and how does it relate to magnetic force?
Magnetic tension is the force per unit area that acts to straighten bent magnetic field lines. It's related to magnetic force in that it represents the restoring force experienced by distorted magnetic fields. Magnetic tension is important in understanding phenomena like waves in plasmas and the dynamics of solar magnetic structures.
47. What is the principle behind magnetic drug targeting, and how does it use magnetic forces?
Magnetic drug targeting is a technique where drugs are attached to magnetic nanoparticles and guided to specific locations in the body using external magnetic fields. The magnetic forces on these particles allow for precise control of drug delivery. This technique relies on the interaction between the applied magnetic field and the magnetic moments of the nanoparticles.
48. How do magnetic forces contribute to the operation of tokamak fusion reactors?
In tokamak fusion reactors, magnetic forces are used to confine and control the hot plasma. A combination of toroidal and poloidal magnetic fields creates a helical field structure that exerts forces on the charged particles, keeping them away from the reactor walls. Additional magnetic fields are used for plasma shaping and stability control, all relying on the precise application of magnetic forces.
49. What is the principle behind magnetohydrodynamic power generation, and how does it use magnetic forces?
Magnetohydrodynamic (MHD) power generation uses the interaction between a conducting fluid (usually a hot ionized gas) and a magnetic field to generate electricity directly. As the conducting fluid moves through a magnetic field, the magnetic force causes charge separation, creating an electric current. This process converts the kinetic energy of the fluid directly into electrical energy without moving parts.
50. How do magnetic forces affect the behavior of magnetic domains in ferromagnetic materials?
In ferromagnetic materials, magnetic forces influence the alignment and movement of magnetic domains. External magnetic fields exert torques on the magnetic moments within domains, causing them to align with the field. As the field strength increases, domains aligned with the field grow at the expense of others through domain wall motion. These processes, driven by magnetic forces, determine the material's overall magnetic behavior.
51. What is the concept of magnetic susceptibility, and how does it relate to magnetic force?
Magnetic susceptibility is a measure of how much a material will become magnetized in response to an applied magnetic field. It's related to magnetic force in that it determines how strongly a material will be attracted to or repelled by a magnetic field. Materials with high positive susceptibility (fer

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