Total charge –Q is uniformly spread along the length of a ring of radius R. A small test charge +q of mass m is kept at the centre of the ring and is given a gentle push along the axis of the ring.
a) show that the particle executes a simple harmonic oscillation
b) obtain its time period
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a) The charge q is displaced by z along the axis of the ring. The force acting on the charge q will be at the centre O. simple harmonic is the motion undertaken by the charge q. Also, charge q is proportional to the z and is directed towards the centre O.
Electric field at the axis of the ring is given as:
The net force on the charge Fnet = qE
Since z << R, we get
b) Time period is given as
When matter experiences a force when placed in a magnetic field, the property of matter is called an electric charge. The field surrounding an electric charge is called an electromagnetic field, where opposite charges attract each other. It is a scalar quantity, and the charge can be either positive or negative in nature. Electric charges are measured in coulombs, and they can be quantised in nature.
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