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Q.

A square non-conducting loop, 20 cm, on a side is placed in a magnetic field. The centre of side AB coincides with the centre of magnetic field. The magnetic field is increasing at the rate of 2 T/s. The potential difference between B and C is

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a

30 mV

b

zero

c

10 mV

d

20 mV

answer is D.

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Detailed Solution

Perpendicular distance between BC and center O is d. From B , select a small element dx at a distance of x.Induced electric field is tangential to circle of radius d2+x2.∫E→.dl→=dϕdt=AdBdt ⇒E2πr=πr2dBdt ⇒E=r2dBdt      here r=d2+x2 Now, from B to C △V=∫Ecosθdx ⇒△V=∫r2dBdt×dr×dx ⇒△V=d2dBdtlBC=0.10220.2=0.02V=20mV
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A square non-conducting loop, 20 cm, on a side is placed in a magnetic field. The centre of side AB coincides with the centre of magnetic field. The magnetic field is increasing at the rate of 2 T/s. The potential difference between B and C is