Coursework 17: FARADAY’S LAW and AC.

1) A flat coil of area 4.5 x 10^-4 m² has 200 turns of wire with total resistance 20 Ω. The coil lies with its area perpendicular to a uniform magnetic field B of magnitude 0.60 T. The coil is connected in series with a resistor of 40 Ω.

a) Evaluate the average emf induced in the circuit if the magnetic field is reduced to zero in a time of 0.10 s.

a) Suppose the field remains constant at 0.60 T and the coil is turned 90⁰ in 0.50 s so that the area of the coil becomes parallel to the magnetic field. What is the average induced current in the circuit? (4 marks)

2) A coil is rotating at constant angular velocity in a uniform magnetic field B of

0.01 T. The B field is perpendicular to the axis of rotation as in the diagram below.

The area of the coil is 2.0 x 10^-4 m² , the number of turns is 50 and the angular speed is 20 revolutions per second.

Evaluate

a) the average induced emf during one complete revolution

b) the r.m.s value of the induced emf

c) the maximum value of the induced emf

d) the induced emf at the instant when the magnetic flux passing through the coil is a maximum

e) the induced emf at the instant when the magnetic flux passing through the coil is zero

f) the induced emf at the instant when the plane of the coil lies at 40⁰ to the field direction. (12 marks)

3) A rectangular loop (3 cm by 5 cm) of wire is partly in a region of uniform magnetic field B of magnitude 0.25 T. The loop is pulled out of the magnetic field at a constant speed of 5 cm s^-1 as shown. The total resistance of the loop is 15 Ω.

.

Calculate the following:

a) Calculate the emf induced in the wire loop.

b) The current in the wire. Use this to find the rate at which energy is lost as heat in the wire.

c) The force F required to pull the loop

d) The power used by the external force in pulling the loop out of the field

(8 marks)

4) A domestic electricity supply has a peak value of 325 V. What is the r.m.s. current in a 100 W light bulb? (2 marks)

5) A 4 Ω resistor is connected across an AC supply of 12 V_r.m.s. with negligible internal resistance. Evaluate

a) the peak value of the potential drop across the resistor

b) the peak value of the current in the resistor

c) the average power dissipated in the resistor.

(6 marks)

6) A metal framed window is 1.3 m high and 0.7 m wide. It hinges about a vertical edge and faces due South. The window is in a location where the horizontal component of the Earth’s field is 20 μT and the vertical component is 50 μT.

a) Calculate the magnetic flux through the closed window.

b) Calculate the average emf induced when the window is opened through an angle of 90⁰ in a time of 0.80 s. (4 marks)

7) A flat circular coil of 120 turns and area 0.070 m² is placed with its axis parallel to a uniform magnetic field. The flux density of the field is changed steadily from

80 mT to 20 mT over a period of 4.0 s. What is the average emf induced in the coil during this time?

(2 marks)

8) A rectangular loop of wire is placed near a long current carrying wire as shown.

If the current is changing at a rate of r amps per second, show that the emf induced in the rectangular coil is given by:

(Hint: first find the flux passing through the coil by considering a thin horizontal strip of thickness dx and length c at a distance x from the wire. Then use integration to find flux through whole of rectangle). (6 marks)

An electric generator consists of a rectangular loop 8 x 5 in a uniform magnetic field of 0.15 T rotating at frequ about an axis perpendicular to the field direction. Find max emf etc

Suggestions

Loop falling out of magnetic field – find terminal velocity

Earth vertical b = 40 microT. Coil of area lies horizontally – pick it up and turn over find average emf.

Date: 2015-12-17; view: 1110