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# Force on a Current Carrying Conductor in a Magnetic Field

May 11, 2023

## Introduction:

A. M. Ampere suggested that a magnetic field can exert mechanical force on a freely suspended current-carrying conductor. We choose a uniform magnetic field to study this force exerted by an external magnetic field on a current-carrying conductor. A magnetic field where magnetic field lines are parallel and equidistant is known as a uniform magnetic field.

Suppose we keep the current-carrying conductor in a uniform magnetic field. In that case, the direction and magnitude of the magnetic field remain the same throughout the dimensions of the current-carrying conductor.

## Experiment: Force on a current-carrying conductor in a magnetic field

We can create a uniform magnetic field using two bar magnets or a horseshoe magnet. The aluminum rod is suspended horizontally by conducting wires between the poles of a horseshoe magnet, and electricity is passed through the wires.

A current-carrying conductor can also exert a magnetic force on a freely suspended magnet placed in its magnetic field and deflect the magnet.

## Observations:

On passing a current through the conductor (aluminum rod) kept in a magnetic field, the conductor gets displaced. On increasing the current in the conductor, the deflection increases (F 𝝰 I).

On changing the direction of the current, the direction of deflection of the rod also changes.

On increasing the magnetic field strength, the deflection also increases. (F 𝝰 B)

The deflection also increases by increasing the length of the conductor placed in the magnetic field. (F 𝝰 L)

The deflection also depends upon the angle (𝞱) between the current in the conductor (I) and the magnetic field (B). (F 𝞪 sin𝞱)

## Fleming’s Left Hand Rule:

Fleming’s left-hand rule is used to know the direction of force experienced by a current-carrying conductor in an external magnetic field. According to this rule, when the thumb, forefinger, and central finger are kept mutually perpendicular to each other, then

Thumb-: Shows the direction of the force.

Forefinger-: Shows the direction of the magnetic field.

Central finger-: Shows the direction of the current.

### Conclusion:

The force “F” experienced by a current-carrying conductor depends on the following factors:

F α Current in the conductor

F α I

F α Magnetic field

F α B

F α Length of the conductor

F α L

F 𝝰 the angle (𝞱) between the current in the conductor (I), and the magnetic field (B)

F 𝞪 sin𝞱

F is maximum when 𝞱 = 90o, F is minimum when 𝞱 = 0

Thus, F α BIL Sin𝞱, As a current-carrying conductor, experiences force in a magnetic field, the same way a charged particle in motion also experiences a force in an external magnetic field. Fleming’s Left-hand rule also gives the direction of the force on a charged particle in an external magnetic field.

• The direction of motion of the positive charge is taken in the direction of the flow of current.
• The direction of motion of the negative charge is opposite to the direction of current flow.

Conclusion: A charged particle in motion experiences a force in an external magnetic field:

Suppose a charge q moves with velocity = v in a magnetic field = B.

If the angle between v and B is θ, it will experience a magnetic force= F.

F = q v B sinθ

When θ = 0, Fmin = 0

and θ = 90o, Fmax = q v B

A charged particle in motion moves in a circular path if it perpendicularly enters an external magnetic field.

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