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Chapter 29: Problem 3

Which of the following will induce a current in a loop of wire in a uniform magnetic field? a) decreasing the strength of the field b) rotating the loop about an axis parallel to the field c) moving the loop within the field d) all of the above e) none of the above

Short Answer

Expert verified
a) Decreasing the strength of the field b) Rotating the loop about an axis parallel to the field c) Moving the loop within the field d) Decreasing the strength of the field and moving the loop within the field Answer: d) Decreasing the strength of the field and moving the loop within the field. Explanation: Both decreasing the strength of the field (option a) and moving the loop within the field (option c) result in a change in magnetic flux, which, according to Faraday's Law, induces a current in the loop. Option b does not lead to induced current because rotating the loop about an axis parallel to the field keeps the angle between the magnetic field and the area vector constant, and thus, the magnetic flux remains unchanged.

Step by step solution

01

Option a: Decreasing the strength of the field

If the strength of the magnetic field decreases, the magnetic flux through the loop will change. According to Faraday's law, this change in magnetic flux will induce a current in the loop. Therefore, the option (a) is correct.
02

Option b: Rotating the loop about an axis parallel to the field

If the loop is rotated about an axis parallel to the field, the angle between the magnetic field and the area vector of the loop remains constant (both are parallel). Thus, the magnetic flux through the loop does not change, and no current will be induced. Therefore, the option (b) is incorrect.
03

Option c: Moving the loop within the field

When the loop moves within the magnetic field, the area of the loop exposed to the field may change. This results in a change in the magnetic flux through the loop. According to Faraday's law, this change in magnetic flux will induce a current in the loop. Therefore, the option (c) is correct. With the above analysis, we can see that both options (a) and (c) lead to induced currents in the loop. Thus, the correct answer is: d) Decreasing the strength of the field and moving the loop within the field.

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Most popular questions from this chapter

A circular coil of wire with 20 turns and a radius of \(40.0 \mathrm{~cm}\) is laying flat on a horizontal table as shown in the figure. There is a uniform magnetic field extending over the entire table with a magnitude of \(5.00 \mathrm{~T}\) and directed to the north and downward, making an angle of \(25.8^{\circ}\) with the horizontal. What is the magnitude of the magnetic flux through the coil?

A solid metal disk of radius \(R\) is rotating around its center axis at a constant angular speed of \(\omega .\) The disk is in a uniform magnetic field of magnitude \(B\) that is oriented normal to the surface of the disk. Calculate the magnitude of the potential difference between the center of the disk and the outside edge.

A circular conducting loop with radius \(a\) and resistance \(R_{2}\) is concentric with a circular conducting loop with radius \(b \gg a(b\) much greater than \(a\) ) and resistance \(R_{1}\). A time-dependent voltage is applied to the larger loop, having a slow sinusoidal variation in time given by \(V(t)=V_{0} \sin \omega t\) where \(V_{0}\) and \(\omega\) are constants with dimensions of voltage and inverse time, respectively. Assuming that the magnetic field throughout the inner loop is uniform (constant in space) and equal to the field at the center of the loop, derive expressions for the potential difference induced in the inner loop and the current \(i\) through that loop.

A square conducting loop with sides of length \(L\) is rotating at a constant angular speed, \(\omega\), in a uniform magnetic field of magnitude \(B\). At time \(t=0\), the loop is oriented so that the direction normal to the loop is aligned with the magnetic field. Find an expression for the potential difference induced in the loop as a function of time.

You have a light bulb, a bar magnet, a spool of wire that you can cut into as many pieces as you want, and nothing else. How can you get the bulb to light up? a) You can't. The bulb needs electricity to light it, not magnetism. b) You cut a length of wire, connect the light bulb to the two ends of the wire, and pass the magnet through the loop that is formed. c) You cut two lengths of wire and connect the magnet and the bulb in series.
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