Problem 21.12 A 650-turn solenoid, 22 cm long, has a diameter of 2.1 cm . A 11-t

ID: 1456669 • Letter: P

Question

Problem 21.12

A 650-turn solenoid, 22 cm long, has a diameter of 2.1 cm . A 11-turn coil is wound tightly around the center of the solenoid.

Part A

If the current in the solenoid increases uniformly from 0 to 4.8 A in 0.70 s , what will be the induced emf in the short coil during this time?

Express your answer to two significant figures and include the appropriate units.

Problem 21.12

A 650-turn solenoid, 22 cm long, has a diameter of 2.1 cm . A 11-turn coil is wound tightly around the center of the solenoid.

Part A

If the current in the solenoid increases uniformly from 0 to 4.8 A in 0.70 s , what will be the induced emf in the short coil during this time?

Express your answer to two significant figures and include the appropriate units.

Given that number of turns is N = 650

Length of the solenoid is L = 22 cm=0.22 m

diameter is d = 2.1 cm

radius of the coil is r = 1.05 cm

Area of the coil is A = pi *r^2 = (3.14)* ( 1.05*10^-2m)^2 = 3.46*10^-4 m^2

Number of turns per unit length is

n = N_1 / L

= 650/ 0.22 m

= 2954 turns / m

Hence, the magnetic field is,

B = ?_0 n I

= 4pi*10^-7 * 2954* 4.8 A = 1.78*10^-2 T

The induced emf

e = N d ? / dt

= 11 * 1.78*10^-2 T * 3.46*10^-4 m^2 / 0.70 s

= 9.7*10-5 V

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