A rectangular loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform megnetic field of magnitude 0.3 tesla directed normal to the loop. What is the voltage developed acorss the cut if velocity of the loop is `1 cm s^(-1)` in a direction normal to the (i) longer side (ii) shorter side of the loop ? For how long does the induced voltage last in each case?

Explanation

Here, `A = 8 xx 2 = 16 cm^(2) = 16 xx 10^(-4) m^(2), B = 0.3` tesla, `upsilon = 1 cm//sec = 10^(2) ms^(-1)`
induced e.m.f. = e = ?
(i) When velocity is normal to longer side,
`l = 8 cm = 8 xx 10^(-2) m`
`e = B l upsilon = 0.3 xx 8 xx 10^(-2) xx 10^(-2)`
`= 2.4 xx 10^(-4) V`
Time, `t = ("distance moved")/("velocity") = (2 xx 10^(-2))/(10^(-2)) = 2` side,
(ii) When velocity is normal to shorter side,
`l = 2 cm = 2 xx 10^(-2) cm`
`e = B l upsilon = 0.3 xx 2 xx 10^(-2) xx 10^(-2) = 0.6 V`
Time, `t = ("distance moved")/("velocity") = (8 xx 10^(-2))/(10^(-2)) = 8 sec`
Note that induced voltage lasts in each case, so long as the loop is partially in the magnetic field.