A magnetic field directed into the page changes with time according to B = 0.027

Question

A magnetic field directed into the page changes with time according to B = 0.027 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) xXX (a) When t3.50s and r20.020 0 m, what is the magnitude of the electric field at point P2? N/C (b) When t3.50 s and r20.020 0 m, what is the direction of the electric field at point P2? into the page out of the page perpendicular to r2 and clockwise perpendicular to r2 and counterclockwise

Explanation / Answer

here r2 =0.02 m and t = 3.50 s

magnetic field is given by,

    B = 0.0270 t2 + 1.40
differentiate the equation on both sides,

dB/dt = 2[ 0.027 ] t = [0.054]*t
the electric field is

E =-(dB/dt)(r2/2)

= -(0.054*t)(r2/2)

= -(0.054*3.5)(0.02/2)

= -1.89 e-3 N/C

magnitude: 1.89e-3 N/C, perpendiculr to r2 and ccw

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