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 0.26 T. The magnetic field has the same direction as the normal to the plane of the coil. The radius increases to 0.34 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 radius of the coil. An emf is induced due to the magnitude of the constant magnetic field. An emf is induced due to the change in magnetic flux. An emf is induced due to the change in area of the coil.

(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 induced emf divided by the time interval the magnetic field divided by the radius of the coil the resistance divided by the induced emf the 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 no induced emf and no induced current because they can exist only if there is a continuous path. There is an induced emf but there is no induced current because the current exists 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. An induced emf and an induced current are present because of the remaining free electrons in the wire.

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

(b) The coil has a resistance of 0.66 . Find the magnitude of the induced current. A

Explanation / Answer

i) induced emf = rate of chage of magnetic flux

emf is induced to the change in magnetic flux

ii) No. The magnitude of the emf depends only on
the magnitude of the rate at which the flux changes.

iii) i = e / R
the induced emf divided by the resistance

iv) There is an induced emf but there is no induced current
because the current exists only if there is a continuous path

a) change in area = pi (0.34^2 - 0.11^2) = 0.325 m^2

induced emf = d(BNA)/dt

B and N are constant.

e = NB dA/dt

= 1 x 0.26 x (0.325 / 0.08) = 1.06 V

b) I = e/R = 1.06 / 0.66 = 1.60 A

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