A straight copper wire of length `0.45 m` is perpendicular to a uniform magnetic field of induction 0.7 T. It is moved at right angles to its length at a speed of 2m/s. (i) Find the induced emf between the ends of the wire. (ii) If the ends of are joined by completing a circuit through a 4-ohm resistor, at what rate must be work be done to keep the wire moving at the constant speed of 2m/s ?

Explanation

Data: `l=2m, B=0.7 T, v=2m//s, R=4 Omega`
(i) The induced emf, E=Blv
`=(0.7)(2)(2) = 2.8 V`
(ii) The induced current, `I=E/R = (2.8)/4 = 0.7A`
The rate at which work must be done = electric power dissipated through the resistor
`=EI= (2.8)(0.7) = 1.96` W