A magnetic field directed into the page changes with time according to B = 0.071

Question

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

B = 0.071 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 = 2.20 s

and

r2 = 0.020 0 m,

what is the magnitude of the electric field at point

P2?

_________N/C

(b) When

t = 2.20 s

and

r2 = 0.020 0 m,

what is the direction of the electric field at point

P2?

perpendicular to r2 and counterclockwise,

out of the page

into the page

perpendicular to r2 and clockwise

Explanation / Answer

a) When r2= 0.02 m=>

r2<r

In such a case, the magentic field is given by-

E= r/2 dB/dt

dB/dt =0.071*2*t =0.071*2*2.20 =0.3124

=> E= 0.02 *(0.3124)/2 =0.003124 N/C

b) when such a case is there where there is a production if electric field due to changing magnetic field, the direction of electric field is generally given by

tangential to the circle pointing counterclockwise =>

The answer should be perpendicular to r2 and in clockwise direction.

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