The figure below shows two circular regions R_1 and R_2 with radii r_1 = 20.6 cm

Question

The figure below shows two circular regions R_1 and R_2 with radii r_1 = 20.6 cm and r_2 = 30.3 cm. In R_1 there is a uniform magnetic field of magnitude B_1 = 50.6 mT directed into the page, and in R_2 there is a uniform magnetic field of magnitude B_2 = 78.0 mT directed out of the page (ignore fringing). Both fields are decreasing at the rate of 10.2 mT/s. Calculate contourintegral vector E middot d s vector for (a) path 1, (b) path 2, and (c) path 3. (a) Number Units (b) Number Units (c) Number Units

Explanation / Answer

Given,

Radii, r1 = 20.6 cm

Radii, r2 = 30.3 cm

Magnetic field, B1 = 50.6 mT

Magnetic field, B2 = 78 mT

a) E . ds = - (d /dt)

so, for path 1 only R1 contribues to flux

(d / dt) = A (dB/dt) = pi x (20.6 x 10-2)2 (-10.2 x 10-3)

so, E . ds = - 1.36 mV

b) for path 2

(d / dt) = A (dB/dt) = pi x (30.3 x 10-2)2 x (- 10.2 x 10-3)

so, E . ds = - 2.94 mV

c) for path 3,

so, E . ds = 2.94 - 1.36 = 1.58 mV

(Please rate my answer if you find it helpful, good luck...)

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