The magnetic field in a particular region is independent of position, but varies

ID: 1320246 • Letter: T

Question

The magnetic field in a particular region is independent of position, but varies in time as sketched in the figure below. If a loop of area

0.98 m2

is oriented perpendicular to this magnetic field, what is the approximate magnitude of the induced emf at

t = 0

and

t = 0.7 s?

(a) Estimate B(0).
T

Estimate B(0.25 s).
T

What is the magnitude of the induced emf at

t = 0?

(Use your estimate/estimates.)
V

(b) Estimate B(0.5 s).
T

Estimate B(0.75 s).
T

What is the magnitude of the induced emf at

t = 0.7 s?

(Use your estimate/estimates.)
V

induced emf is defiend as the rate of change of magnetic flux

in mathematical form,

induced emf e = NAdB/dt or NABW

where A = area

N = no. of tunrs

W = angular frequency

dB/dt = rate of change of amgnetic flux

part A: at 0, B is 0

---------------

part B :

at 0.25, dB/dt = 0.5/0.5 = 1

emf e = 1 * 0.98 * 1 = 0.98 volts

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so indcued emf is zero
------------------------------------

B at 0.5 is 0.5 Tesla
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B at 0.7 is 0.4 tesla ( apprx)

so induced emf = 1 * 0.98 * 0.4/0.7

emf e = 0.56 Tesla

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