Question

A train is moving from south to north with a velocity of $90$ km/h. The vertical component of earth's magnetic induction is $0.4\times {10}^{-4}Wb/m^2.$ If the distance between the two rails is $1m,$ what is the induced e.m.f. in its axle?

• A. $1mV$
• B. $0.1mV$
• C. $10mV$
• D. $100mV$

Answer 1

The correct option is A $1mV$

By taraday's law,

Einduced - $\frac{-d\varphi }{dt}$

$\varphi =\overrightarrow{B}.\overrightarrow{A}=|\overrightarrow{B}||\overrightarrow{A}|cos\theta$

Here $\theta =0$ so,

$\varphi =B.A$

$\frac{-d\varphi }{dt}=\frac{dB.A}{dt}=\frac{-BdA}{dt}-\frac{AdB}{dt}$

As B is constant, $\frac{dB}{dt}=0$

$=\frac{d\varphi }{dt}=\frac{-B.dA}{dt}$

Here, $\frac{dA}{dt}=\frac{dlb}{dt}=\frac{ldb}{dt}+\frac{bdl}{dt}$

b(breadth) of the train is not

changing it a length that is going

into the field is varying with speed

90km/h(25m/s),so.

$\frac{dA}{dt}=l\left(0\right)+bv=\left(1\right)\left(25\right)=25$

so,$\frac{d\varphi }{dt}=-\left(0.4\right)\times {10}^{-4}\times 25={10}^{-3}v$

Einduced =${10}^{-3}v=1mv$

Option - A is correct.