Question

**Using Faraday’s Law equation, answer the following
mathematical questions.**

A plane circular loop of conducting wire has a radius r = 8m and N = 4 turns. It is located in a uniform magnetic field. The magnetic field’s direction makes a 75° angle with respect to the normal of the loop. The magnitude of magnetic field B increases at a constant rate from B1 = 3.2 T to B2 = 4.7 T in a time interval of t =5s. If the resistance of the loop is R = 12.5 W, how much current flows around the loop as the magnetic field is increased?

**What is the area of the loop?**

**What is the component of the magnetic field
perpendicular to the loop?**

**What is the initial magnetic flux of the
loop?**

**What is the final flux of the loop?**

**What is the time rate of change of the
flux?**

**What is the emf generated around the loop?**

**Using your previous knowledge of Ohm’s Law, what is the
current that flows around the loop in response to the
EMF?**

Answer #1

A two-turn circular wire loop of radius 0.737 m lies in a plane
perpendicular to a uniform magnetic field of magnitude 0.591 T. If
the entire wire is reshaped from a twoturn circle to a one-turn
circle in 0.116 s (while remaining in the same plane), what is the
magnitude of the average induced emf E in the wire during this
time? Use Faraday’s law in the form E = − ∆(N Φ) ∆t . Answer in
units of V.

A circular loop of wire of radius R lies in the
xy-plane, where a time-varying, radially symmetric
magnetic field of magnitude B = k r
t3 (in SI units) points in the
positive z-direction. Here, t is time, r
is the distance from the centre of the loop, and k is a
positive constant.
(i) What must be the SI units of k ?
(ii) Calculate the magnetic flux Φm through the loop
as a function of time t. ...

Which of the following is/are TRUE?
a. Faraday’s law of electromagnetic induction states that the
induced emf or current in a circuit is directly proportional to the
time rate of change of the magnetic flux in the circuit
b. There is induced emf or current in a circuit of the magnetic
field in the circuit is very high
c. There is induced emf or current in a circuit if the area of
the circuit is not too big
d. There...

A time-varying magnetic field is perpendicular to the plane of a
circular loop of diameter 10 cm made with wire of diameter 3.4 mm
and resistivity 2.07 × 10-8?·m.
The magnetic field increases as a function of time, with magnitude
B = (0.79 t) T/s
a) What is the magnitude of the emf induced in the loop?
b) What is the value of the current through the loop?
c) At what rate does energy appear as thermal energy in the...

6: A single-turn circular loop of wire rests flat on this page.
A magnetic field is directed perpendicular to this page pointing
outwards (towards you). When the magnetic field strength increases
from 3.2 T to 6.5 T in 0.026 seconds, a 1 V emf is induced in the
coil.
a) Calculate the radius of the loop.
b) State the direction of the induced current and briefly
explain how you arrived at your answer.

Inducing Voltage and Current
A circular conducting loop of radius 21.0 cm is located in a
region of homogeneous magnetic field of magnitude 0.900 T pointing
perpendicular to the plane of the loop. The loop is connected in
series with a resistor of 137 Ω. The magnetic field is now
increased at a constant rate by a factor of 2.60 in 13.0s.
Calculate the magnitude of the induced emf in the loop while the
magnetic field is increasing.
Calculate the...

A circular conducting loop of radius 31.0 cm is located in a
region of homogeneous magnetic field of magnitude 0.300 T pointing
perpendicular to the plane of the loop. The loop is connected in
series with a resistor of 109 Ω. The magnetic field is now
increased at a constant rate by a factor of 2.40 in 15.0s.
1) Calculate the magnitude of the induced emf in the loop while
the magnetic field is increasing.
2) Calculate the magnitude of...

1.
A rectangular loop of wire with sides 0.142 and 0.528 m lies in
a plane perpendicular to a constant magnetic field (see part
a of the drawing). The magnetic field has a magnitude of
0.604 T and is directed parallel to the normal of the loop's
surface. In a time of 0.104 s, one-half of the loop is then folded
back onto the other half, as indicated in part b of the
drawing. Determine the magnitude of the average...

A circular conducting loop of radius 31.0 cm is located in a
region of homogeneous magnetic field of magnitude 0.100 T pointing
perpendicular to the plane of the loop. The loop is connected in
series with a resistor of 211 Ω. The magnetic field is now
increased at a constant rate by a factor of 2.80 in 17.0s.
1.) Calculate the magnitude of the induced emf in the loop while
the magnetic field is increasing.
2.) Calculate the magnitude of...

A circular loop of wire lies in the x-y plane and has a radius
of 7.50 cm. There is a uniform B field in the z direction with a
sinusoidal varying strength of B_o sin?(?t) Where B_o=1.7*?10?^(-6)
T and the frequency f is 1200 kHz. What is the angular frequency of
the B-field? What is the period of a single cycle for the B-field?
What is the maximum flux in the coil of wire? What is the minimum
flux in...

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