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  • Tell me? - A conducting circular loop made of a thin wire, has area and resistance . It is placed perpendicul - Electromagnetic Induction and Alternating currents - JEE Main

A conducting circular loop made of a thin wire, has area 3.5\times 10^{-3}m^{2}  and resistance 10\Omega. It is placed perpendicular to a time dependent magnetic field B(t)=(0.4T)sin(50\pi t). The field is uniform in space. Then the net charge flowing through the loop during t=0\, s\; \; and\: \: t=0\, ms is close to :

  • Option 1)

    14\: mC\; \; \;

  • Option 2)

    7\: mC\; \; \;

  • Option 3)

    21\: mC\; \; \;

  • Option 4)

    6\: mC\; \; \;

Answers (1)

best_answer

 

Induced Charge -

dq= i.dt= \frac{-N}{R}\frac{d\phi }{dt}.dt

dq= \frac{-N}{R}d\phi

 

- wherein

Induced Charge time independent

 

q = \frac{\Delta \phi }{R} = \frac{1}{10} \left ( B_{f} - B_{i} \right )A

= \frac{1}{10} \times 3.5 \times 10^{-3} \left [ 0.4 sin 50 \pi \times 10^{-2} -0 \right ]

= 1.4 x 10-4

= 0.14 mc


Option 1)

14\: mC\; \; \;

Option 2)

7\: mC\; \; \;

Option 3)

21\: mC\; \; \;

Option 4)

6\: mC\; \; \;

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