Question

Consider a loop of wire and a uniform magnetic field as shown below. The loop is shown at five different times as it travels to the right through the magnetic field. The loop is perpendicular toC the field. t5 1. Using the right-hand rule for each side (a, b, c d) of the loop, determine the direction of in- duced emf for each of the five times above. t4 ts hong side b: t1 A0ng t2 t3 2. Using your answers to item 1, determine the direction (clockwise/coun- terclockwise) of the current flow for each of the five times.

Answer 1

The law of electromagnetic induction states that the induced emf $\epsilon =-d\phi /dt$ where $\phi$ is the magnetic flux through the loop.

For time t₁:The loop is outside the magnetic field . Therefore $d\phi /dt=0$. There is no emf and no current through the loop.

For time t₂:

The loop is entering the field. Therefore the magnetic flux is increasing . Therefore from Lenz's law the induced emf is such that it causes the magnetic flux through the loop to decrease . Therefore the induced emf is in the clockwise direction and current also is in the clockwise direction.

For time t₃:

The magnetic field is the same for this case i.e it is neither increasing nor decreasing. Therefore the emf is zero and current also is zero.

For time t₄:

The flux is decreasing. Therefore from Lenz'z law the induced emf is in the counterclocwise direction and the current is also in the same direction.

For time t₅:

The emf is zero and current is also zero.