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 X 10^(-5) T`. (a) Find the average emf induced across the width 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

As the train moves in a magnetic field, a motional emf epsilon = vBi is produced across its width
Here B is the component fof the magnetic field in a direction perpendicular to the plane of the motion, i
e
the vertical component
The speed of the train is `v = (960km)/(16h) =16
67 ms^(-1)` Thus `epsilon = (16
67 ms^(-1) (4
0 X10^(-5) T)(1
30m)` =8
6 X 10^(-4) V`
The leakage current is i = epsilon/R and the retarding force is ` F= ilB = (8
6 X 10^(-4) V)/(100 Omega) X1
3 m X 4
0 X 10^(-5) T = 4
47 X 10^(-10) N