A horizontal telephone wire 1 km long is lying along east-west in earth's magnetic field. If falls freely to the ground from a height of 10 m. Calculate the e.m.f. induced in the wire on striking the ground. Given horizontal component of earth's field is 0.32 gauss.

Explanation

Here, `l = 1 km = 10^(3) m`.
Let us calcualte velocity of wire on striking the ground. From `upsilon^(2) - u^(2) = 2 a s`
`upsilon^(2) - 0 = 2 xx 9.8 xx 10 = 196`
`upsilon = sqrt(196) = 14 ms^(-1)`
As velocity at the start of the fall is zero, therefore, average velocity of wire,
`upsilon' = (0 + 14)/(2) = 7 ms^(-1)` and `B = 0.32 G = 0.32 xx 10^(-4) T`
As `e = B l upsilon'` `:. e = 0.32 xx 10^(-4) xx 10^(3) xx 7 = 0.224 V`