A circular coil of radius 0.11 m contains a single turn and is located in a cons

Question

A circular coil of radius 0.11 m contains a single turn and is located in a constant magnetic field of magnitude 0.35 T. The magnetic field has the same direction as the normal to the plane of the coil. The radius increases to 0.38 m in a time of 0.080 s.

Concepts:
(i) Why is there an emf induced in the coil? (Select all that apply.)

An emf is induced due to the change in magnetic flux.An emf is induced due to the change in area of the coil.An emf is induced due to the change in radius of the coil.An emf is induced due to the magnitude of the constant magnetic field.

(ii) Does the magnitude of the induced emf depend on whether the area is increasing or decreasing? Explain.

Yes. An increase in area will cause the magnitude of the emf to be larger than a decrease in area.No. The magnitude of the emf depends only on the magnitude of the rate at which the flux changes.    

(iii) What determines the amount of current induced in the coil?

the magnetic field divided by the radius of the coilthe induced emf divided by the time interval    the resistance divided by the induced emfthe induced emf divided by the resistance

(iv) If the coil is cut so it is no longer one continuous piece, are there an induced emf and an induced current? Explain.

There is an induced emf but there is no induced current because the current exists only if there is a continuous path.An induced emf and an induced current are present because of the remaining free electrons in the wire.    There is no induced emf and no induced current because they can exist only if there is a continuous path.There is an induced current but there is no induced emf because the emf exists only if there is a continuous path.

Calculations:
(a) Determine the magnitude of the emf induced in the coil.
V

(b) The coil has a resistance of 0.73 . Find the magnitude of the induced current.
A

Explanation / Answer

(i)

An emf is induced due to the change in area of the coil.
Flux = B x dA, it is directly depends on the change in area

(ii)

.No. The magnitude of the emf depends only on the magnitude of the rate at which the flux changes.
Note: The direction of the current flow depends on it.

(iii)

the induced emf divided by the resistance.
This is basic Ohm's law, I = V/R

(iv)

There is no induced emf and no induced current because they can exist only if there is a continuous path.

(a)

V = d/dt[flux]
flux = B dA
V = B (dA/dt)
dA = pi(rf2 - ri2)
r i = 0.11 m. r f = 0.38 m
= 0.454 - 0.038 = 0.416 m2
dA/dt = 0.416/0.08 = 5.2
B = 0.35 T
V = 0.35 x 5.2 = 1.82 V

(b)

Current, I = V/R = 1.82 / 0.73 = 2.5 A

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