A small bar magnet drops through a coil. The magnet docs not rotate during the f
ID: 1493831 • Letter: A
Question
A small bar magnet drops through a coil. The magnet docs not rotate during the fall. Assume that both the starting point and the end point are very far away from the coil. What is the initial magnetic flux in the coil? What is the final magnetic flux through the coil? What is the net change of the magnetic flux in the coil? Would the falling magnet induce any voltage in the coil? Does the induced voltage depend on the average magnetic flux change or on the instantaneous value of the magnetic flux change? 2. A circular loop of wire is placed in a uniform, constant magnetic field. What orientation of the loop would have the maximum magnetic flux in the loop? For what orientation is the flux zero? Justify your answers.Explanation / Answer
Q1. mangetic fields of a bar magnet are closed loops , starting from north pole and ending at south pole.
when the magnet is falling through a coil,
i)
as starting point is very far away, it can be safely assumed that no magnetic flux is linking the coil
ii) similarly , as the end point is very far away, no magnetic flux is linking at the end point.
iii)as there are no magnetic flux linking the coil in the beginning as well as in the end, net change=0-0=0
iv)when the faling magnet is sufficient close to the coil so that magnetic flux linking the coil is non-zero, due to the motion of the magnet,
it will induce emf in the coil as per faraday law.
v)emf induced=rate of change of flux linking the coil at the moment
hence it depends upon the instantaneous rate of change of flux.
Q2. magnetic flux linkage=integration of B.dS
where "." represents the dot product.
B=magnetic flux density
dS=area vector
as area vector is perpendicular to the surface of the coil and dot product is maximum when two vectors have 0 degree as angle between them,
when dS is orieinted along the B vector, maximum flux will be linking the coil
hence the coil should remain perpendicular to the magnetic flux vector in order to ensure maximum flux linkage happens.
with similar arguments as above, when coil is parallel to the magnetic flux vector, zero flux linkage will occur.
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