A bicycle si resting on its stand in the east-west direction and rear wheel is rotating at `100` revolution per minute. Length of each spoke is `30 cm`, and vertical component of earth's magnetism is `1.5 xx 10^(-5)` tesla. If the emf induced in the spokes is `3 pi xx 10^(-6)V`, the angle of dip will be :

Options

A. `tan^(-1)((3)/(4))`
B. `tan^(-1)((1)/(sqrt(3)))`
C. `tan^(-1) (sqrt(3))`
D. `tan^(-1)((1)/(3))`

Answer

A

Explanation

The bicylce is resting in east-west direction, therefore horizontal magnetic field lines of earth's magnetisation will cut across the spokes of the wheel. Let this horizontal field of earth's magnetism is `B_(H)`. The induced emf between the axle and the rim of the wheel is `e = (1)/(2)B_(H)l^(2) omega`
`:. B_(H) = 2 xx 10^(-5)T`
given `B_(v) = 1.5 xx 10^(-5)T`. Angle of dip
`theta = tan^(-1)((B_(v))/(B_(H)))`