Magadh express takes 16 hours to cover the distance of 960km between patna and Gaziabad. The rails are separated by 130 cm and the vertical component of the earth's magnetic field is `4.0 xx 10^(-5)` T.
(a) Find the average emf induced across the witdh of the train.
(b) If the leakage resistance between the rails is 100 Omega, find the retarding force on the train due to magnetic field.

Explanation

Here, `r = 0.10 mm B = 20 mT = 20 xx 10^(-3) T`
`upsilon = 10 m//s , e = ?`
In a small time dt, let the semi-circuar wire more through a small distance dx (in or out of the field). Fig
As `e = (d phi)/(dt) = (d)/(dt) (B xx A) = B (dA)/(dt)`
`:. e = (B (2 r dx))/(dt) = 2 B r upsilon`
`2 xx 20 xx 10^(-3) xx 0.1 xx 10`
`= 0.40 V`