Okay, 90% of this is nonsense besides the numbers maybe.
The solution for the problem is:
1 Watt = 1 Joule per second
1 Watt*second = 1 Joule
a Kilowatt is 1,000 Watts
an hour is 60 seconds times 60 minutes or 3,600 seconds
a Kilowatt * hour is 1,000 Watts in 3,600 seconds
15 W*h = 15,000 Watt*hour = 15,000 Watt * 3,600 seconds = 54,000,000
Watt*second
54,000,000 Watt*second = ? Joules
54,000,000 Joules / second = 54,000,000 Watts
In the above case we can say that power given by external agent to pull the rod must be equal to the power dissipated in the form of heat due to magnetic induction.
Part a)
when we pull the rod with constant speed then power required will be product of force and velocity
here we will have

P = 4 W
v = 4 m/s
now we will have


So external force required will be 1 N
PART B)
now in order to find magnetic field strength we can say

here we know that induced EMF in the wire is E = vBL
so power due to induced magnetic field is given by


by solving above equation we will have
