Question

A cylindrical bar magnet is kept along the axis of a circular coil. If the magnet is rotated about its axis, then
A. current will be induced in the coil.
B. no current will be induced in the coil.
C. only emf will be induced in the coil.
D. an emf and current both will be induced in the coil.

Answer 1

Bar magnet is a magnet which has poles. First to understand the set-up we can draw a diagram. From the diagram we can understand the field lines. Then by using the formula for the magnetic flux and the induced emf we can draw a conclusion whether an emf or current will be induced in a coil or not.

Formula used:

& \phi =B\cdot A \\\ & \varepsilon =\dfrac{d\phi }{dt} \\\ \end{aligned}$$ **Complete answer:** A simple diagram for the set-up is given as follows  Here we can see that a cylindrical bar magnet is kept along the circular coil. The direction in which the cylindrical bar magnet rotates is shown by ω which denotes the angular velocity. As the cylindrical bar magnet is rotating along its own axis the magnetic field won’t change. That implies $$B=\text{constant}$$ Magnetic flux is given as the dot product of the magnetic field and the cross sectional area. Suppose cross-sectional area of circular coil is A and magnetic field B, then the magnetic flux is given as $$\phi =B\cdot A$$ As both quantities, magnetic field and cross-sectional area, are constant therefore $$\phi =\text{constant }$$ Now the induced emf is the rate of change of flux with respect to time and it is expression is $$\varepsilon =\dfrac{d\phi }{dt}$$ As magnetic flux is constant, its derivative will be zero and so the induced emf. $$\varepsilon =0$$ As there is no induced emf, there will be no current flowing through the circular coil. **So, the correct answer is “Option B”.** **Note:** In case the bar magnet was kept perpendicular to the axis of circular coil, then the magnetic field will be changing. As the magnetic field will be changing, the flux will change too and so there will be an emf induced in the coil. Due to induced emf, current will also be flowing through the coil. Hence in such case there will be induced emf and current both.