Question

A spatially uniform magnetic field is restricted in a circular region of space with radius of 2.5 cm and has a constant ...


A spatially uniform magnetic field is restricted in a circular region of space
with radius of 2.5 cm and has a constant direction; see figure below. If the
magnetic field varies with time t as B(t) = (25 mT/s^2)t^2, what is the magnitude of the induced electric field at a distance of 4.00 cm from the center of the magnetic field region at t = 2 s?

Transcribed: magnetic field region K. 4.00 cm X, XX

Answer

Given,Radius of within which the magnetic flux exist, r1 = 2.5 cmTime varying magnetic field,  B =25 mTs2t2r2 = 4.00 cmt = 2 s

We know the magnetic flux changes from the loop is,

φ = B .daφ = 25 mTs2t2daφ = 25 mTs2t2πr12

Now according to Faraday's law,

E.dl = -dφdtE2πr2 = -ddt25 mTs2t2πr12E2πr2 = -25 mTs2t2πr12ddtt2E = -25×10-3r122r22tE = -25×10-3tr12r2

Now the induced electric field in the loop of radius r = 4 cm at time t = 2 s

E = -25tr12r2E = -25×10-3×2×2.50 ×10-224.00×10-2E = -78.125×10-5 NC

Negative sign indicates that the induced emf oppose the change of the magnetic flux.

magnitude of the electric field,

E = 78.125×10-5 NC

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