1) A solenoid with 1200 turns per meter has a diameter of 7.00 cm. A current I =
ID: 1401260 • Letter: 1
Question
1)
A solenoid with 1200 turns per meter has a diameter of 7.00 cm. A current I = 2.51 A flows in the counterclockwise direction (when viewed from location P) in the solenoid. A rectangular loop of length L = 16.0 cm, width w = 12.5 cm, and 2 turns is centered on the axis of the solenoid.
(a) Find the magnitude of the magnetic flux through one turn of the rectangular loop.
Wb
(b) When the current is increased to 5.47 A, the magnitude of the induced emf in the rectangular loop is 116 mV. How long did it take for the current to get to this value?
ms
Explanation / Answer
givn
number of turns per unit length n = 1200 turns / m
current i = 2.51 A
magnetic field inside the solenoid B = uo*n*i = 4*3.14*10^-
7*1200*2.51 = 3.78*10^-3 T
magnetic flux = phi = B*A
A = area = pi*r^2
r = radius of the solenoid = 3.5 cm
phi = 3.78*10^-3*3.14*0.035^2 = 1.45*10^-5 Wb <<-------answer
+++
part(b)
emf = rate of change in flux
change in flu of the rectangular coil = N*dB*A
d phi = N*uo*n*(i2-i1)*A
d phi = 2*4*3.14*10^-7*1200*(5.47-2.51)*3.14*0.035^2
d phi = 3.43*10^-5 Wb
emf = 116 mv
dt = d phi / emf = (3.43*10^-5)/(116*10^-3) = 0.3 ms <<-------answer
++
2)
total flux through the coil= phi = N*B*A*(cos0 - cos90)
A = area of the circular coil = pi *r^2
r = radius of the coil = r = 10 cm = 0.1 m
emf induced = flux/time
emf = (1027*4.53*10^-5*3.14*0.1^2)/(10*10^-3) = 0.146 v <<<------answer
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