A rectangular loop of wire is placed in the XY-plane with its side of length 3 cm parallel to the X-axis and the side of length 4 cm parallel to the Y-axis. It is moving in the positive X-direction with the speed 10 cm/s. A magnetic field exists in the space with its direction parallel to the Z-axis. The field decreases by `2xx10^(-3) ` T/cm along the positive X-axis and increases in time by `2 xx 10^(-2)` T/s. The induced emf in the wire is

Options

A. `-4.8 xx 10^(-5) V`
B. `4.8 xx 10^(-5) V`
C. 0
D. `3.6 xx 10^(-5) V`

Answer

C

Explanation

Induced emf in wire = Rate of change of flus
` = (d)/(dt) (BA) = A { ((d)/(dt) B) + v (d)/(dx) B}`
` = 12 xx 10^(-4) (2 xx 10^(-2) + 10 xx 10^(-2) xx 2 xx 10^(-3) )`
` = 12 xx 10^(-4) (2 xx 10^(-2) + 2 xx 10^(-4) )`
` = 24 xx 10^(-4) (10^(-2) + 10^(-4) ) = 24 xx 10^(-5) V`
` = 0.000024 V = 0 V`