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

G1 Physics · Accepted Answer

dΦ/dt = ∫0^R B₀(1−r²/R²)2πrdr = πB₀R²/2. At radius 2R, E(4πR)=πB₀R²/2, so E=B₀R/8.