A very long solenoid of inner radius 4.25 cm creates an oscillating magnetic field B of the form B = B m a x cos (ω t) For this solenoid, B max = 0.00275 T and ω = 349 rad/s. What is the maximum value E max of the induced electric field at a perpendicular distance 1.85 cm from the axis of the solenoid?

Question

Physics

Howard Peck

11 August, 02:29

A very long solenoid of inner radius 4.25 cm creates an oscillating magnetic field B of the form B = B m a x cos (ω t) For this solenoid, B max = 0.00275 T and ω = 349 rad/s. What is the maximum value E max of the induced electric field at a perpendicular distance 1.85 cm from the axis of the solenoid?

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Braxton Garner · Answer 1

Flux

Φ = B A

= πR²B

-dΦ / dt = - πR²dB / dt

EMF = - πR².00275d. cos (ω t) / dt

EMF = (πR².00275/ω) sin ω t

EMFmax = (πR².00275/ω)

EMFmax = ∫ E dR, E is elecreic field at distance R from the axis

= 2πR X E

(πR².00275/ω) = 2πR X Emax

Emax = R x. 00275/2ω

= 1.85 x 10⁻² x. 00275 / (2 x 349)

=.7288 x 10⁻⁷ N/C

= 7.288 x 10⁻⁸ N/C