Question

A student is giving a presentation to a class describing magnetic and electric fields in a region of space. First, the student describes what happens when there is a constant magnetic field in the region of space. Then, the student describes what happens when there is a time-dependent magnetic field in the region of space. Which of the following a correct description by the student abo what occurs when the magnetic field changes from being constant to being time dependent?

a. When the magnetic field is constant, there is only a magnetic field in the region of space. When the magnetic field is time dependent, there will be both a magnetic field and an electric field in the region of space.
b. When the magnetic field is constant, there will be both a magnetic field and an electric field in the region of space. When the magnetic field is time dependent, there is only a magnetic field in the region of space.
с. In both situations, there will be both a magnetic field and an electric field in the region of space. In both situations, there will only be a magnetic field in the region of space. If the magnetic field is not constant over the region, then there will be both a magnetic field and an electric field in the region of space
d. In both situations there will only be a magnetic field in the region of space. If the magnetic field is not constant over the region, there will still be only a magnetic field in the region of space.

Answer 1

a. When the magnetic field is constant, there is only a magnetic field in the region of space. When the magnetic field is time dependent, there will be both a magnetic field and an electric field in the region of space.

Step-by-step explanation:

This is true because according to Maxwell's equation, a time dependent magnetic field produces an electric field.

When the magnetic field is constant, there is no electric field in that region of space. But, when it begins to vary, an electric field is then generated by Maxwell's equation which is given by

CurlE = -dB/dt

So, there is initially no electric field when the magnetic field is constant, but it exists when the magnetic field becomes time dependent.

So when dB/dt = 0

CurlE = 0 ⇒ E = 0

So when dB/dt ≠ 0

CurlE ≠ 0 ⇒ E ≠ 0