1. A coil of 500 turns shrinks from 800 square centimeters to 600 in just ten se
ID: 1613399 • Letter: 1
Question
1. A coil of 500 turns shrinks from 800 square centimeters to 600 in just ten seconds due to deformation. What is the uniform, constant magnetic field directed through the coil if the change in area induces a 20 mV difference between the coil's ends while it shrinks, and which way is the field directed as seen from a side of the coil where the induced current is clockwise?
2. A uniform magnetic field in the upward direction is, during one interval, decreasing according to the equation B=2exp(-7t) mT. Find the induced current at t=100 ms in a circular ring with a radius of 10 cm and a resistance of 5 ohms if the ring's axis is tilted sixty degrees with respect to the field vector, and also state which way the current circulates in the ring as viewed from above.
Explanation / Answer
1)
magnetic flux = N*B*A
induced emf = -rate of change in flux
emf = -N*B*dA/dt
dA = A2 - A1
A2 = 600 cm^2 = 600*10^-4 m^2
A1 = 800 cm^2 = 800*10^-4 m^2
emf = 20 mV = 0.02 V
N = 500
0.02 = 500*B*(600*10^-4 - 800*10^-4)/10
B = 0.02 T
clockwise
===============
2)
magnetic flux = B*A*costheta
emf = -rate of change in flux
emf = -B*A*(costheta2 - costheta1)/dt
theta = 0
theta 2 = 60 degrees
emf = -2*e^-(7*0.1)*pi*0.1^2*(cos60-cos0)/0.1
emf = 0.156 V
current I = emf/R = 0.0312 A <<<<--------answer
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