Magnetic flux and induced emf

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Question

A uniform magnetic field B = 0.5 T exists in a circular region of radius R = 5 m. A loop of radius R = 5 m encloses the magnetic field at t = 0 and then pulled at uniform speed v = 2 ms^-1 in the plane of the paper. Find the induced emf (in V) in the loop at time t = 3 s.

Moderate

Solution

$O_{1} M = (vt - R) + (\frac{2 R - vt}{2}) = \frac{v}{2}$
$l = PN = 2 \sqrt{R^{2} - {(O_{1} M)}^{2}} 2 \sqrt{R^{2} - {(\frac{vt}{2})}^{2}} = \sqrt{4 R^{2} - v^{2} t^{2}}$
so $E = Bvl = Bv \sqrt{4 R^{2} - v^{2} t^{2}}$
given $R = 5 m, v = 2 m / s, t = 3 s$
$E = 0.5 \times 2 \sqrt{4 \times 25 - 4 \times 9} = 8 V$

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Magnetic flux and induced emf

Unlock the full solution & master the concept.

A uniform magnetic field B = 0.5 T exists in a circular region of radius R = 5 m. A loop of radius R = 5 m encloses the magnetic field at t = 0 and then pulled at uniform speed v = 2 ms-1 in the plane of the paper. Find the induced emf (in V) in the loop at time t = 3 s.

O1M=vt-R+2R-vt2=v2l=PN=2R2-O1M22R2-vt22=4R2-v2t2so E=Bvl=Bv4R2-v2t2given R=5m, v=2m/s, t = 3sE=0.5×24×25-4×9=8V

Ready to Test Your Skills?

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A uniform magnetic field B = 0.5 T exists in a circular region of radius R = 5 m. A loop of radius R = 5 m encloses the magnetic field at t = 0 and then pulled at uniform speed v = 2 ms^-1 in the plane of the paper. Find the induced emf (in V) in the loop at time t = 3 s.