A solenoid of length 30.0 cm is made of 11000 circular coils. It carries a stead

Question

A solenoid of length 30.0 cm is made of 11000 circular coils. It carries a steady current of 10.0 A . Near its center is placed a small, flat, circular metallic coil of 250 circular loops, each with a radius of 1.00 mm . This small coil is oriented so that it receives half of the maximum magnetic flux. A switch is opened in the solenoid circuit and its current drops to zero in 25.0 ms .

a) What was the initial flux through the small coil?

b) Determine the average induced emf in the small coil during the 25.0 ms .

c) If you look along the long axis of the solenoid so that the initial 10.0 A current is clockwise, determine the direction of the induced current in the small inner coil during the time the current drops to zero.

d) During the 25.0 ms , what was the average current in the small coil, assuming it has a resistance of 0.250 ?

Explanation / Answer

number of turns in solenoid = 11000

length of the solenoid = L = 0.3 m

magnetic field at the centr of the oil = B = uo*(N/L)*i = 4*3.14*10^-7*(11000/0.3)*10 = 0.46 T

given coil reeives only half of the maximum magnetic flux

area of the circular coil = pi*r^2 = 3.14*0.001^2 = 3.14*10^-6 m^2

maximum magnetic flux = B*A

part ( a )

magnetic flux through the circular coil phi_i =(1/2)*B*A = 0.7222*10^-6 Wb <-----------answer

part(b)

induced emf = rate of change in magnetic flux

given final fluxx = phi_f = 0

time taken = 25*10^-3 s

emf = (phi_f - phi_i)/t

emf = 0.0288*10^-3 v   <-----------answer

part(c)

from lenz law = emf = -dphi/dt

the direction of induced current in the coil is clockwise

part(d)

current = emf/Resistance

current = i = 0.1152 mA <-----------answer

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