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A square loop of side a is placed in same plane as a long straight wire carrying current i amp the center of the loop is at a distance r from hte wire r>> a the loop is moved away from the wire with a constant velocity v The induced emf of the loop is Please give detailed solution rates assured Ans ( not i a^2 v)/ (2 r^2)


A square loop of side a is placed in same plane as a long straight wire carrying current i amp
 
the center of the loop is at a distance r  from hte wire r>> a
the loop is moved away from the wire with a constant velocity v
 
The induced emf of the loop is
 
Please give detailed solution rates assured
 
Ans   (not i a^2 v)/ (2r^2)


Grade:10

1 Answers

ROSHAN MUJEEB
askIITians Faculty 829 Points
2 years ago
Magnetic field the straight wire of currentiiat a distancerrisB=μ0i2πrB=μ0i2πr
flux associated with the loop isϕ=BA=μ0i2πra2ϕ=BA=μ0i2πra2
∴e=−dϕdt=−μ02πia2ddt(1r)=−μ02πia2(−1r2)drdt∴e=-dϕdt=-μ02πia2ddt(1r)=-μ02πia2(-1r2)drdt
Hence the induced emf in the loop is
e=μ02πia2r2v(∵dr/dt=v)

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