A magnetic field directed into the page changes with time according to B= o.053

Question

A magnetic field directed into the page changes with time according to B= o.053 ot^2 + 1.40, where B is in teslas and t is in seconds. The field has a circular cross section of radius R =2.50 cm (see figure below). When t= 3.30 s and r_2= 0.020 0 m, what is the magnitude of the electric field at point P_2? N/C When t =3.30 s and r_2= 0.020 0 m, what is the direction of the electric field at point P_2? into the page perpendicular to r_2 and clockwise perpendicular to r_2 and counterclockwise out of the page

Explanation / Answer

Here ,

B = 0.053* t^2 + 1.40

dB/dt = 0.053 * 2 * t

at t =3.3 s

dB/dt = 0.053 * 2 * 3.3 T/s

Now, for the electric field P2

2 pi * r * E = pi * r^2 * dB/dt

E = 0.020/2 * 0.053 * 2 * 3.3

E = 3.49 *10^-3 N/C

the electric field at P2 is 3.49 *10^-3 N/C

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