Question

A physicist works in a laboratory where the magnetic field is 2 T. She wears a necklace enclosing an area 100 $c{m}^{{}^2}$ of field and having a resistance of 0.1 $\Omega$.Because of power failure the field decays to 1 T in millisecond. The electric charge circulated in the necklace assuming that the magnetic field is perpendicular to area coverd by the neeklace is

• A. 0.01
• B. 0.001
• C. 0.1 C
• D. 1.0 C

Answer 1

The correct option is C 0.1 C

The magnetic field decays by $\Delta B=1.2=(-)1T$ in time $\Delta t={10}^{-3}s,$

through the loop of area $A=100c{m}^2={10}^{-2}{m}^2$.

Hence, the induced emf in loop is :-

$E=A\frac{\Delta B}{\Delta t}={10}^{-2}\times \frac{-1}{{10}^{-3}}=10v.$ (magnitude)

as resistance $R=0.1\Omega$, current flowed,

$I=\frac{E}{R}=\frac{10}{0.1}=100A$.

$\therefore$ The charge flowed in the time $△t$,

$Q=I\Delta t=100\times {10}^{-3}=0.1C$ (Ans)