A uniform magnetic field B exists in a cylindrical region, shown dotted in figure. The magnetic field increases at a constant rate dBdt . Consider a circle of radius r coaxial with the cylindrical region. Find the magnitude of the electric field E at a point on the circumference of the circle.

A∮E¯.d¯l=−AdBdt E∮dl=−AdBdt E(2πr)=−πr2dBdt E=−r2dBdt |E|=r2dBdt

A uniform magnetic field B exists in a cylindrical region, shown dotted in figure. The magnetic field increases at a constant rate dBdt . Consider a circle of radius r coaxial with the cylindrical region. Find the magnitude of the electric field E at a point on the circumference of the circle.

A∮E¯.d¯l=−AdBdt E∮dl=−AdBdt E(2πr)=−πr2dBdt E=−r2dBdt |E|=r2dBdt

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A uniform magnetic field B exists in a cylindrical region, shown dotted in figure. The magnetic field increases at a constant rate $\frac{dB}{dt}$ . Consider a circle of radius r coaxial with the cylindrical region. Find the magnitude of the electric field E at a point on the circumference of the circle.

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\frac{r}{3} \frac{dB}{dt}

\frac{r}{2} \frac{dB}{dt}

\frac{dB}{dt}

\frac{r}{2}

answer is B.

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A \oint \bar{E} . \bar{d} l = - A \frac{dB}{dt}

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$E \oint d l = - A \frac{dB}{dt}$

$E (2 π r) = - π r^{2} \frac{dB}{dt}$

$E = - \frac{r}{2} \frac{dB}{dt}$

$| E | = \frac{r}{2} \frac{dB}{dt}$

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A uniform magnetic field B exists in a cylindrical region, shown dotted in figure. The magnetic field increases at a constant rate dBdt . Consider a circle of radius r coaxial with the cylindrical region. Find the magnitude of the electric field E at a point on the circumference of the circle.

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