A magnetic field in a certain region is given by B = B_ocos(ωt) k and a coil of radius a with resistance R is placed in the x-y plane with its centre at the origin in the magnetic field. Find the magnitude and the direction of the current at (a, 0, 0) at t = π/2ω, t = π/ω and t = 3π/2ω

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Payal Gupta | Contributor-Level 10

8 months ago

This is a short answer type question as classified in NCERT Exemplar

$\emptyset = B . A = B A c o s θ$

$\emptyset = B_{o} π a^{2} c o s w t$

But according to faraday's law e= B_{o $π a^{2} w s i n w t$}

So the current will be I=B_{0 $\frac{π a^{2} w s i n w t}{R}$}

For t= $\frac{π}{2 w}$

I= $\frac{B_{o} π a^{2} w}{R}$ along j

Sinwt= sin(w $\frac{π}{2 w}$ ) = sin $\frac{π}{2}$ =1

T= $\frac{π}{w}$ , I= $\frac{B (π a^{2}) w}{R}$

Sinwt=sinw $\frac{π}{w}$ = sin $π = 0$

T= $\frac{3 π}{2 w}$

I= $\frac{B_{o} π a^{2} w}{R}$

So it become sin $\frac{3 π}{2 w}$ =-1

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A magnetic field in a certain region is given by B = Bocos(ωt) k and a coil of radius a with resistance R is placed in the x-y plane with its centre at the origin in the magnetic field. Find the magnitude and the direction of the current at (a, 0, 0) at t = π/2ω, t = π/ω and t = 3π/2ω

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A magnetic field in a certain region is given by B = B_ocos(ωt) k and a coil of radius a with resistance R is placed in the x-y plane with its centre at the origin in the magnetic field. Find the magnitude and the direction of the current at (a, 0, 0) at t = π/2ω, t = π/ω and t = 3π/2ω