College Physics

Physics & Astronomy

Quiz 6 :

Induced Voltages and Inductance

Quiz 6 :

Induced Voltages and Inductance

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A spacecraft orbiting Earth has a coil of wire in it. An astronaut measures a small current in the coil, although there is no battery connected to it and there are no magnets in the spacecraft. What is causing the current
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Faraday's law of induction states that the instantaneous electromotive force (emf) induced in the circuit is equal to the negative rate of the change in the magnetic flux through the coil. img Here, img is the number of coils, img is the rate of change of the magnetic flux.
Use the Faradays law of induction, then the change in the magnetic flux in the coil will produce an emf.
When the spacecraft orbiting earth, then it will moves from one region of magnetic field strength to another region of magnetic field strength. Hence, the changing the magnetic field through the coil in the spacecraft induces as emf. Due to this reason, there is a current in the coil.

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A uniform magnetic field of magnitude 0.50 T is directed perpendicular to the plane of a rectangular loop having dimensions 8.0 cm by 12 cm. Find the magnetic flux through the loop.
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The expression for the magnetic flux through the loop which is placed in the magnetic field is, img Here, B is the strength of the magnetic field, A is the area of cross-section of the loop, and img is the angle between the magnetic field and the normal to the plane of the loop.
The expression for the area of the rectangular loop is, img Here, l  is the length of the loop, and b is the breadth of the loop.
Substitute 12 cm for l , and 8.0 cm for b in img . img Thus, the area of the rectangular loop is img Substitute 0.50 T for B , img for A , and img in img . img Therefore, the flux through the loop whose plane is perpendicular to the magnetic field is img .

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Does dropping a magnet down a copper tube produce a current in the tube Explain.
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Lenz's law says that the induced magnetic field should be directed in such a way that it opposes the original cause that produces it. If the bar magnet approaches the coil, there will be change in the magnetic flux through the coil. Thus, the induced current in the coil will be directed in such a way that the magnetic field produced due to the induced current opposes the cause that produces it.
Assume the copper tube as a set of coils which are stacked together. If the bar magnet approaches the tube, there will be change in magnetic flux through the tube due to which the current is induced in it. This current will be directed along the circumference of the tube.

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Find the flux of Earth's magnetic field of magnitude 5.00 × 10 5 T through a square loop of area 20.0 cm 2 (a) when the field is perpendicular to the plane of the loop, (b) when the field makes a 30.0° angle with the normal to the plane of the loop, and (c) when the field makes a 90.0° angle with the normal to the plane.
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A circular loop is located in a uniform and constant magnetic field. Describe how an emf can be induced in the loop in this situation.
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A circular loop of radius 12.0 cm is placed in a uniform magnetic field. (a) If the field is directed perpendicular to the plane of the loop and the magnetic flux through the loop is 8.00 × 10 3 T · m 2 , what is the strength of the magnetic field (b) If the magnetic field is directed parallel to the plane of the loop, what is the magnetic flux through the loop
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A loop of wire is placed in a uniform magnetic field. (a) For what orientation of the loop is the magnetic flux a maximum (b) For what orientation is the flux zero
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A long, straight wire carrying a current of 2.00 A is placed along the axis of a cylinder of radius 0.500 m and a length of 3.00 m. Determine the total magnetic flux through the cylinder.
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As the conducting bar in Figure CQ20.5 moves to the right, an electric field directed downward is set up. If the bar were moving to the left, explain why the electric field would be upward.
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A long, straight wire lies in the plane of a circular coil with a radius of 0.010 m. The wire carries a current of 2.0 A and is placed along a diameter of the coil. (a) What is the net flux through the coil (b) If the wire passes through the center of the coil and is perpendicular to the plane of the coil, what is the net flux through the coil
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How is electrical energy produced in dams (That is, how is the energy of motion of the water converted to AC electricity )
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A 400-turn solenoid of length 36.0 cm and radius 3.00 cm carries a current of 5.00 A. Find (a) the magnetic field strength inside the coil at its midpoint and (b) the magnetic flux through a circular cross- sectional area of the solenoid at its midpoint.
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Wearing a metal bracelet in a region of strong magnetic field could be hazardous. Discuss this statement.
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A cube of edge length = 2.5 cm is positioned as shown in Figure P20.7. There is a uniform magnetic field throughout the region with components B x = +5.0 T, B y = +4.0 T, and B z = +3.0 T. (a) Calculate the flux through the shaded face of the cube. (b) What is the total flux emerging from the volume enclosed by the cube (i.e., the total flux through all six faces)
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As the bar in Figure CQ20.5 moves perpendicular to the field, is an external force required to keep it moving with constant speed
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Transcranial magnetic stimulation (TMS) is a noninvasive technique used to stimulate regions of the human brain. A small coil is placed on the scalp, and a brief burst of current in the coil produces a rapidly changing magnetic field inside the brain. The induced emf can be sufficient to stimulate neuronal activity. One such device generates a magnetic field within the brain that rises from zero to 1.5 T in 120 ms. Determine the induced emf within a circle of tissue of radius 1.6 mm and that is perpendicular to the direction of the field.
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Eddy currents are induced currents set up in a piece of metal when it moves through a nonuniform magnetic field. For example, consider the flat metal plate swinging at the end of a bar as a pendulum, as shown in Figure CQ20.9. (a) At position 1, the pendulum is moving from a region where there is no magnetic field into a region where the field img in is directed into the paper. Show that at position 1 the direction of the eddy current is counterclockwise. (b) At position 2, the pendulum is moving out of the field into a region of zero field. Show that the direction of the eddy current is clockwise in this case. (c) Use right-hand rule number 2 to show that these eddy currents lead to a magnetic force on the plate directed as shown in the figure. Because the induced eddy current always produces a retarding force when the plate enters or leaves the field, the swinging plate quickly comes to rest.
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Three loops of wire move near a long straight wire carrying a current as in Figure P20.9. What is the direction of the induced current, if any, in (a) loop A, (b) loop B, and (c) loop C.
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A bar magnet is dropped toward a conducting ring lying on the floor. As the magnet falls toward the ring, does it move as a freely falling object Explain.
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The flexible loop in Figure P20.10 has a radius of 12 cm and is in a magnetic field of strength 0.15 T. The loop is grasped at points A and B and stretched until its area is nearly zero. If it takes 0.20 s to close the loop, what is the magnitude of the average induced emf in it during this time
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