Connect a battery to a solenoid A cylindrical solenoid 48 cm long with a radius

Question

Connect a battery to a solenoid A cylindrical solenoid 48 cm long with a radius of 3 mm has 200 tightly-wound turns of wire uniformly distributed along its length (see the figure). Around the middle of the solenoid is a two-turn rectangular loop 3 cm by 2 cm made of resistive wire having a resistance of 120 ohms. One microsecond after connecting the loose wire to the battery to form a series circuit with the battery and a 20 resistor, what is the magnitude of the current in the rectangular loop and its direction (clockwise or counter-clockwise in the diagram)? (The battery has an emf of 9 V.) clockwise counter-clockwise 20

Explanation / Answer

(A) B = u0 n I

flux through loop = (B) (2)( pi 0.003^2)

induced emf = d(flux)/dt

= (2 u0 n pi 0.003^2) dI/dt

= (2 x 4pi x 10^-7 x (200/0.48) pi 0.003^2) (9/(20 x 1 x 10^-6))

= 0.0133 volt

I = e /R = 0.01333 / 120

I = 1.11 x 10^-4 A

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