Rotating coil in a magnetic field[SOLVED]

According to the mark scheme the answer to this is D - but how? I don't understand this, an explanation would be appreciated.

(edited 1 month ago)

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Eimmanuel

Study Forum Helper

Original post

by tigrispanthera

According to the mark scheme the answer to this is D - but how? I don't understand this, an explanation would be appreciated.

The picture describes how the magnetic flux changes when the area of a coil rotates in an uniform magnetic field. Note that there is a normal vector $\hat{n}$ to the area, the general magnetic flux relationship is BA cosθ, where θ is the angle between the normal vector and magnetic field vector.
When the normal vector and magnetic field vector are parallel, magnetic flux = BA and when they are anti-parallel, magnetic flux = ‒BA.

Going back to your question.
The question states that there is a magnetic field perpendicular to the plane of the coil in the position shown in the diagram.
Assume that the magnetic field is pointing out of the paper and the normal vector is out of the paper, so initially, the magnetic flux is BA or ϕ.
After the coil is rotated through an angle of π radians, the normal vector is pointing into the paper while the magnetic field is still out of the paper, so the magnetic flux is -BA or -ϕ.
The change in magnetic flux linkage is
‒Nϕ ‒ Nϕ = ‒2Nϕ
We can ignore the minus sign, it does not change the physics.
The minus appears because of the way we choose the direction of the magnetic field.
If we choose the initial direction of the magnetic field to be into the paper, then the minus sign will not appear.