Question

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

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

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.

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.

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.