# A magnetic field is described by B? =B0k^sin?t, where B0 = 1.3 T and ? = 20 s?1 . A conducting...

## Question:

A magnetic field is described by {eq}\vec{B} {/eq} {eq}=B_0\hat k \ sin\omega {/eq}t, where B0 = 1.3 T and {eq}\omega {/eq} = 20 s-1 . A conducting loop with area 160 {eq}cm^{2} {/eq} and resistance 9.0 {eq}\Omega {/eq} lies in the x-y plane.

Part A

Find the induced current in the loop at t=0.

Part B

Find the induced current in the loop at t = 0.14 s.

## Faraday's Law of Electromagnetic Induction:

According to Faraday's law, whenever magnetic flux passing through a coil changes, an EMF is induced in the coil, and the magnitude of the induced EMF is equal to the rate of change of magnetic flux i.e.

{eq}\varepsilon =-\displaystyle \frac{d \phi}{dt}\\ {/eq}

where;

• {eq}\phi= B\cdot A {/eq} is the magnetic flux passing through the coil.
• B is the magnetic field in which the coil is kept
• {eq}\varepsilon {/eq} is the induced EMF in the coil

Given:

• Magnetic field {eq}\vec{B} = B_0\hat k \sin \omega t {/eq}, where {eq}B_0 = 1.3\ T {/eq} and {eq}\omega = 20 s^{-1} {/eq}.
• Area of the...

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