A 310 turn solenoid with a length of 19.0 cm and a radius of 1.80 cm carries a c

Question

A 310 turn solenoid with a length of 19.0 cm and a radius of 1.80 cm carries a current of 1.90 A. A second coil of four turns is wrapped tightly around this solenoid, so it can be considered to have the same radius as the solenoid. The current in the 310 turn solenoid increases steadily to 5.00 A in 0.900 s.

(a) Use Ampere's law to calculate the initial magnetic field in the middle of the 310 turn solenoid.
T

(b) Calculate the magnetic field of the 310 turn solenoid after 0.900 s.
T

(c) Calculate the area of the 4-turn coil.
m2

(d) Calculate the change in the magnetic flux through the 4-turn coil during the same period.
Wb

(e) Calculate the average induced emf in the 4-turn coil.
V

Explanation / Answer

a.)B=u0*N*I/L=4*pi*10^-7*310*1.9/0.19=3.89 x 10^-3 T

b.)B=u0*N*I/L=4*pi*10^-7*310*5.0/0.19=0.01025 T

c.)A=pi*0.018*0.018=1.018 x10^-3 m^2

d.)change in flux=A*(B2-B1)=1.018 x10^-3*(0.01025 - 3.89 x 10^-3)=6.464 x10^ -6 T-m^2

e.)V=N*d(flux)/dt=310*(6.464 x10^-6)/0.9=2.23 x10^-3 V= 2.23 mV

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