Question

A 37-turn circular coil of
radius 4.60 cm and resistance 1.00 Ω is placed
in a magnetic field directed perpendicular to the plane of the
coil. The magnitude of the magnetic field varies in time according
to the expression *B* = 0.010
0*t* + 0.040 0*t*^{2},
where *B* is in teslas and *t* is in
seconds. Calculate the induced emf in the coil
at *t* = 4.20 s.

Answer #1

The area of a circular coil of radius r is .

Given the magnetic field passing through the coil is

The magnetic flux passing through area **A** in
presence of uniform magnetic field **B** is

where the area vector is directed normal to the area, is the angle that the magnetic field makes with the area vector or with the normal of the area. Since the magnetic field is normal to the coil, the angle between them is zero. . The magnetic flux passing through a single turn of the coil is

There are 37 turns in the coil, the magnetic flux passing through the coil is

The magnitude of the emf induced in the coil is given by flux rule

Given radius is r=4.60cm=0.046m, and we want to find the induced emf at time t=4.20 seconds.

A 29-turn circular coil of radius 3.40 cm and resistance 1.00 Ω
is placed in a magnetic field directed perpendicular to the plane
of the coil. The magnitude of the magnetic field varies in time
according to the expression B = 0.010 0t + 0.040
0t2, where B is in teslas and
t is in seconds. Calculate the induced emf in the coil at
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A magnetic field is perpendicular to the plane of a single-turn
circular coil. The magnitude of the field is changing, so that an
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wire is then re-formed into a single-turn square coil, which is
used in the same magnetic field (again perpendicular to the plane
of the coil and with a magnitude changing at the same rate). What
(a) emf and (b) current are...

9. A magnetic field is perpendicular to the
plane of a single-turn circular coil. The magnitude of the field is
changing, so that an emf of 0.77 V and a current of 2.7 A are
induced in the coil. The wire is then re-formed into a single-turn
square coil, which is used in the same magnetic field (again
perpendicular to the plane of the coil and with a magnitude
changing at the same rate). What emf is induced in the...

A circular coil of radius 4.0 cm, resistance 0.30 Ω, and 100
turns is placed in a uniform magnetic field at an angle of 30° with
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according to ?(?)=20?^(−0.3?) (in Tesla, t is time in seconds).
What is the value of the current induced in the coil at the time t
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A 149-turn circular coil of radius 2.67 cm is immersed in a
uniform magnetic field that is perpendicular to the plane of the
coil. During 0.153 s the magnetic field strength increases from
51.1 mT to 99.3 mT. Find the magnitude of the average EMF, in
millivolts, that is induced in the coil during this time
interval.

A 133 turn circular coil of radius 2.77 cm is immersed in a
uniform magnetic field that is perpendicular to the plane of the
coil. Over an interval of 0.121 s, the magnetic field strength
increases from 55.7 mT to 95.9 mT. Find the magnitude of the
average emf avgEavg induced in the coil during this time interval,
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avg=Eavg= ?

A circular coil of 312 winds of wire (radius = 7.0 cm,
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A coil 5.00 cm in radius, containing 250 turns, is
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B = (0.230 T/s)t + (4.00 x 10-5
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A 20-turn coil with a diameter of 6.00 cm is placed in a
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The field remains constant thereafter.
1) What is the magnitude of the induced emf in the coil at t
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