Inside a long cylindrical region of radius R, the axial magnetic field is B(r, t)=B₀t(1-r²/R²), and it is zero outside. Determine the induced electric-field magnitude at radius 2R.
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Inside a long cylindrical region of radius R, the axial magnetic field is B(r,t)=B₀t(1−r²/R²), and it is zero outside. Determine the induced electric-field magnitude at radius 2R.

G1 Physics · Accepted Answer

The flux-rate through the full magnetic region is ∫0^R B₀(1−r²/R²)2πrdr=πB₀R²/2. At radius 2R, E(4πR)=πB₀R²/2, hence E=B₀R/8.