A coil with 270 turns, a radius of 3.8cm , and a resistance of 20? surrounds a s

Question

A coil with 270 turns, a radius of 3.8cm , and a resistance of 20? surrounds a solenoid with 240turns/cm and a radius of 3.6cm (Figure 1) . The current in the solenoid changes at a constant rate from 0 to 2.7A in 0.30s .

Calculate the magnitude of the induced current in the coil.

Express your answer using two significant figures.

A coil with 270 turns, a radius of 3.8cm , and a resistance of 20? surrounds a solenoid with 240turns/cm and a radius of 3.6cm (Figure 1) . The current in the solenoid changes at a constant rate from 0 to 2.7A in 0.30s . Calculate the magnitude of the induced current in the coil. Express your answer using two significant figures.

Explanation / Answer

Magnetic field inside the solenoid is

B = mu_o N I

Flux through the coil is

flux = N' B A

Emf inducediin the coil is

emf = d( BA) / dt

= mu_o N N' A dI / dt

= ( 4 pi *10^ -7 ) ( 270) ( 24000) ( pi)( 3.8*10^ -3 m)^2 ( 2.7 ) / ( 0.3 )

=3.32*10^ -3 V

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