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