A single loop of wire with an area of 0.0900m2 is in a uniform
magnetic field...
A single loop of wire with an area of 0.0900m2 is in a uniform
magnetic field that has an
initial value of 3.8 T, is perpendicular to the plane of the loop,
and is decreasing at a
constant rate of 0.190 T/s.
(a) What emf is induced in this loop?
(b) If the loop has a resistance of 0.600O, find the current induced in the loop.
Solutions
Expert Solution
Concepts and reason
The concept to be used in this problem is of Faraday’s Law of Electromagnetic Induction.
First, apply Faraday’s Law of Electromagnetic Induction law to find the emf induced in the loop. Then, using the voltage-current relation find the current flowing in the loop.
Fundamentals
The Law of Electromagnetic Induction states that the emf induced in the closed circuit is equal to the change in the magnetic flux through the circuit.
ε=−NdtdϕB
Here N is the number of turns of the coil and ϕB is the magnetic flux.
The expression of magnetic flux is given by,
ϕB=BA
Here B is the magnitude of the magnetic field and A is the area of the surface.
The voltage-current relation is given by the Ohm's law:
I=RV
Here V is the emf induced in the loop and R is the resistance of the loop.
(a)
The Law of Electromagnetic Induction states that the emf induced in the closed circuit is equal to the change in the magnetic flux through the circuit.
ε=−NdtdϕB
Here N is the number of turns of the coil and ϕB is the magnetic flux.
Substitute BA for ϕm ,
ε=−Ndtd(BA)=−NAdtdB
Substitute 1 for N , 0.09m2 for A and 0.19T⋅s−1 for dtdB ,
ε=−(1)(0.09m2)(0.19T⋅s−1)=−0.0171V=−1.71×10−2V
Hence the magnitude of the induced emf is 1.71×10−2V .
(b)
The current flowing in the loop is given by,
I=Rε
Here ε is emf induced in the loop and R is the resistance of the loop.
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