Find expression for electric field given B(t)

mkematt96 · Nov 25, 2016

Cross-section diagram of a uniform magnetic field region, shown as a green disk of radius R with inward-pointing dots labeled B, inside a larger circle; an orange circular path of radius r carries a line element dl, with E field arrows drawn around the outer circle, and a solved answer box showing E = (RB0 e^(-t/tau))/(2 tau) marked incorrect.

Homework Statement

See picture above

Homework Equations

Int (E dot dl) = Int (B dot dA)

The Attempt at a Solution

Where did I go wrong? Is there a sign error possibly or am I off conceptually? [/B]

Handwritten physics derivation on lined paper: B(t) = B0 e^(-t/tau), Faraday's law integral of E dot dl = -d/dt of integral of B dot dA, then -E 2 pi R = dB/dt pi R^2, leading to E = -R/2 dB/dt and a final boxed result for E.

Charles Link · Nov 25, 2016

The only thing I see that is incorrect is in your relevant equations (2), it should say ## -dB/dt ## instead of ## B ##. Their ## dl ## in the figure is in the opposite direction of what it should be, but I don't think that is your mistake. The line integrals in these Stoke's formulas always go counterclockwise with +z out of the paper. Perhaps the instructor wanted you to spot that anomaly, etc...

Find expression for electric field given B(t)

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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