A long solenoid has 1400 turns per meter of length, and it carries a current of 3.0 A. A small circular coil of wire is placed i
nside the solenoid with the normal to the coil oriented at an angle of 90.0˚ with respect to the axis of the solenoid. The coil consists of 56 turns, has an area of 1.2 × 10-3 m2, and carries a current of 0.70 A. Find the torque exerted on the coil.
2 answers:
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(a) 0.0068 Wb
Since the plane of the coil is perpendicular to the magnetic field, the magnetic flux through the coil is given by
where
N = 200 is the number of loops in the coil
B is the magnetic field intensity
is the area of the coil
At the beginning, we have
so the initial magnetic flux is
at the end, we have
so the final magnetic flux is
So the magnitude of the change in the external magnetic flux through the coil is
(b) 0.567 V
The magnitude of the average voltage (emf) induced in the coil is given by Faraday-Newmann law
where
is the variation of magnetic flux
is the time interval
Substituting into the formula, we find
(c) 0.142 A
The average current in the coil can be found by using Ohm's law:
where
I is the current
V is the voltage
R is the resistance
Here we have:
V = 0.567 V (induced voltage)
(resistance of the coil)
Solving for I, we find