Question

A flat coil of $500$ turns, each of area $50c{m}^2$, rotates in a uniform magnetic field of $0.1Wb/m^2$ about an axis normal to the field at an angular speed of $150rad/s$. (Initially magnetic field was along the area vector of the field). The coil has a resistance of $15\Omega$. Maximum induced current in the coil is

• A. $1.5A$
• B. $2.5A$
• C. $3.5A$
• D. $4.5A$

Answer 1

The correct option is B $2.5A$


Flux through the coil $\varphi =N\overrightarrow{B}.\overrightarrow{A}$
$=NBA\cos \theta$

We can write $\theta =\omega t$ because coil is rotating with uniform angular speed.

i.e $\varphi =NBA\cos \omega t$

As the coil rotates, the angle made by the area vector with the magnetic field changes and so, the flux changes. Emf induced
$ϵ=-\frac{d\varphi }{dt}$
$=NBA\omega \sin \omega t$

Current induced in the coil
$i=-\frac{1}{R}\frac{d\varphi }{dt}$
$=\frac{NBA\omega }{R}\sin \omega t$

The variation of current with time is depicted by the following graph.



Here, maximum value of current $=i_0$
$=\frac{NBA\omega }{R}=\frac{500\times 0.1\times 50\times {10}^{-4}\times 150}{15}$
$=2.5A$