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

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. Let us learn about magnetic power by answering questions such as what is magnetic force and understanding magnetic force definition with magnetic force formula and some magnetic force examples.

Define magnetic force:

Consider a point charge ‘q’ placed in both magnetic and electric fields. The magnitude of the magnetic field is given by B(r) and the magnitude of the electric field is given by E(r). 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. F_E+F_M , where F_E is the electric force and F_M 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.

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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)].

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

NCERT Physics Notes:

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• 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 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.
• 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 the parallel direction to the magnetic field is zero.

Right-hand thumb rule:

If the current flowing conductor is held by the right hand, the direction facing by 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. Mathematical expression for this law is given as

F ∝ m₁m₂/µ₀r²

F =k m₁m₂/µ₀r²

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.

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Magnetic force due to current carrying conductor:

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. The overall amount of charge carriers is given by nAI, where I denote the current flowing through the conductor. Let the drift velocity of every mobile carrier be V_d. When the conductor is placed in some external magnetic field B, the applied force on the moving charges is written as F=(nAI)_qV_d ✖ B, here the nkVd is the current density and it can be written as J.

F=(AI.J) ✖ B = Il✖ B.

F = Il✖ B or BIlsinθ

From this article, we learnt about magnetic force, its properties and features, Magnetic force by current-carrying current and so on related to the Magnetic force topic. Let us discuss some frequently asked questions about magnetic force in class 11 and class 12.

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