The current generator I g , shown in figure, sends a constant current i through the circuit. The wire ab has a length ℓ and mass m and can slide on the smooth, horizontal rails connected to I 4 . The entire system lies in a vertical magnetic field B. Find the velocity of the wire as a function of time.

Question

Philoid · Accepted Answer

Given:

Initial current = i

Length of sliding wire ab = l

Mass = m

Magnetic field = B

Formula used:

Magnetic force on the wire ab … (i), where i = current, l = length of sliding wire, B = magnetic field

Now, velocity v can be written as … (ii), where u = initial velocity = 0(in this case), a = acceleration, t = time.

Hence, acceleration a = v/t … (iii)

Now, according to Newton’s 2nd law of motion, … (iv), where F = force, m = mass, a = acceleration.

Substituting (iii) in (iv) and equating (i) and (iv), we get

⇒

Hence, velocity of the wire as a function of time is (Ans)