Force on a current carrying conductor in a magnetic field

We can obtain the equation for the Force on a current-carrying conductor in a magnetic field using the formula of the force on a moving charge in a magnetic field.

Force on a current-carrying conductor in a magnetic field – formula

We have seen in one of our posts, that Fon a moving charge = q (v X B). [ read this post here: formula of the force on moving charge in a magnetic field ]

q (v X B) formula can be modified in the following way to get the formula for the Force on a current-carrying conductor in a magnetic field.

derivation of the formula

The following steps will help us to derive the equation for the Force on a current-carrying conductor in a magnetic field.

F = q (v X B) = (I t) [(L/t) x B ] …. (1)

Here, we have replaced charge q with the product of current I in the conductor and the time duration t. We have also replaced velocity v with L/t where L is the length of the current-carrying conductor (hence, the displacement of charge) and t is again the time duration being considered.

From (1) we get:

F = I L x B (where IL can be taken as the current element)

F = I L x B

Force on a current carrying conductor in a magnetic field (formula derivation)

F = I L B Sin θ

where θ is the angle between the current element and the magnetic field.

The maximum value of the Force on a current-carrying conductor in a magnetic field

When θ = 90 degrees, then the force on a current-carrying conductor in a magnetic field becomes maximum and it is expressed as Fmax = I L B

The minimum value of the Force on a current-carrying conductor in a magnetic field

When θ = 0 degrees, then the force on a current-carrying conductor in a magnetic field becomes minimum and it is expressed as Fmin = 0

Force on a current carrying conductor in a magnetic field
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