The current generator Ig, 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 I4. The entire system lies in a vertical magnetic field B. Find the velocity of the wire as a function of time.
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)