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Question

A long solenoid has 1000 turns per meter and its radius is R=2.5 cm. Current in the solenoid increases at a rate of 200π A/s. Find the magnitude of induced electric field at a point outside the solenoid at a distance 4 cm from its axis.


A
3×104 V/m
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B
6.25×104 V/m
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C
4.5×104 V/m
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D
9.25×104 V/m
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Solution

The correct option is B 6.25×104 V/m
The induced electric field is obtained from expression:
 Edl=dϕdt
At point B at distance r from centre of solenoid (outside it),
E(2πr)cos0=ddt(BScos0) ...(i)
since induced electric field is tangetial along circumference (θ=0), and area direction along B hence angle between B & S i.e  θ=0

R=2.5×102 m
E(2πr)=πR2dBdt
E=(R22rdBdt) ...(ii)
Now, for solenoid
B=μ0ni
dBdt=μ0n(didt) ...(iii)
putting the values,
dBdt=(4π×107×1000×(200π)
dBdt=8×102
From Eq (ii),
E=(2.5×102)22×4×102×8×102
E=6.25×104 V/m

Physics

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