A magnetic field directed into the page changes with time according to B = 0.063

Question

A magnetic field directed into the page changes with time according to

B = 0.063 0t2 + 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).

(a) When

t = 2.90 s

and

r2 = 0.020 0 m,

what is the magnitude of the electric field at point

P2?

N/C

(b) When

t = 2.90 s

and

r2 = 0.020 0 m,

what is the direction of the electric field at point

P2?

out of the pageinto the page    perpendicular to r2 and clockwiseperpendicular to r2 and counterclockwise

Explanation / Answer

As

B = 0.0630t^2 + 1.40,

then

dB/dt = 0.1260t

From Faraday's law,

E(2 pi r2) = -(pi r2^2)(0.1260t)

Solving for |E|,

|E| = |-0.0630 r2 t| = 3.65*10^-3 N/C   [ANSWER, PART A]

********************

By right hand rule, it is COUNTERCLOCKWISE.

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