If a closed loop lies partially inside and partially outside a region of changing magnetic field, which is true about the induced electric field along the path?
A It is zero at points on the path outside the region of changing magnetic field.
B It is zero at points on the path inside the region of changing magnetic field.
C It is zero at all points on the path.
D It is zero at no points on the path.
The correct answer and explanation is:
The correct answer is A: It is zero at points on the path outside the region of changing magnetic field.
According to Faraday’s Law of Induction, an electric field is induced in a closed loop when there is a time-varying magnetic flux passing through the loop. This law states that the induced electromotive force (EMF) is proportional to the rate of change of magnetic flux through the loop. Mathematically, it is expressed as: E=−dΦBdt\mathcal{E} = -\frac{d\Phi_B}{dt}
where ΦB\Phi_B is the magnetic flux.
For a closed loop that lies partially inside and partially outside a region with a changing magnetic field, the induced electric field will only be non-zero in regions where there is a change in the magnetic field. This is because a time-varying magnetic field produces an electric field according to Faraday’s Law, and the induced electric field depends directly on the spatial region where the magnetic flux is changing.
Inside the region of changing magnetic field, the induced electric field is non-zero, as the magnetic flux is changing over time. The electric field will loop around the changing magnetic field, in a direction according to Lenz’s Law (to oppose the change in flux).
Outside the region of changing magnetic field, the magnetic flux is constant (or zero), so no electric field is induced in this area. The electric field along the path outside the region of the changing magnetic field will be zero, because there is no time-varying magnetic field to generate an electric field.
Thus, the induced electric field is non-zero inside the region of the changing magnetic field but zero outside. Therefore, the correct answer is A.