Question

Scientists studying an anomalous magnetic field find that it is inducing a circular electric field in a plane perpendicular to the magnetic field. The electric field strength 1.5 m from the center of the circle is 5.5 mV/m.

Answer 1

Answer:

$\frac{dB}{dt} = 7.33 \times 10^{-3} T/s$

Explanation:

As we know that the changing magnetic field will induce the electric field in the plane perpendicular to the magnetic field

As per Faraday's law the induced EMF is given as

$EMF = \frac{d\phi}{dt}$

$EMF = \pi r^2 \frac{dB}{dt}$

now we also know that induced EMF is given as

$EMF = \int E.dr$

$EMF = E.(2\pi r)$

now we know that

$E(2\pi r) = \pi r^2\frac{dB}{dt}$

$E = \frac{r}{2}(\frac{dB}{dt})$

so we have

$5.5 \times 10^{-3} = \frac{1.5}{2}(\frac{dB}{dt})$

$\frac{dB}{dt} = 7.33 \times 10^{-3} T/s$