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A positive charge $\mathrm{Q}$ is uniformly distributed along a circular ring of radius $\mathrm{R}$. A small test charge $\mathrm{q}$ is placed at the centre of the ring figure. Then,
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if $\mathrm{q}>0$ and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre
,
if $\mathrm{q} < 0$ and is displaced away from the centre in the plane of the ring, it will never return to the centre and will continue moving till it hits the ring,
if $q < 0$, it will perform $S H M$ for small displacement along the axis
if $\mathrm{q}>0$ and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre
,
if $\mathrm{q} < 0$ and is displaced away from the centre in the plane of the ring, it will never return to the centre and will continue moving till it hits the ring,
if $q < 0$, it will perform $S H M$ for small displacement along the axis
The main concepts are used
(i) Interaction between charges.
(ii) Stable and unstable equilibrium.
The positive charge $\mathrm{Q}$ is uniformly distributed at the-outer surface of the ring. Thus, electric field inside the sphere is zero.
Then the positive charge of the ring will interact equally a charge placed at centre of ring will be in unstable equilibrium.
So the effect of electric field on charge q due to the positive charge $Q$ is zero.
Now, there are two forces are active between charges $(Q$ and q).
(i) attractive force. (ii) repulsive force.
There are two cases obtained :
Case I : When charge $q>0$ i.e., $q$ is a positive charge, there creates a repulsive force between charge $q$ and $Q$.
The repulsive forces of charge $Q$ from all around the charge $q$ will push it towards.ihe centre if it is displaced from the centre of the ring.
Case II : When charge $q < 0$ i.e., $q$ is a negative charge then there is an attractive force between charge $Q$ and $q$.
If $\mathrm{q}$ is displaced slightly small from the centre then the positive charges nearer to this charge will attract it towards itself and charge q will never return to the centre.
(i) Interaction between charges.
(ii) Stable and unstable equilibrium.
The positive charge $\mathrm{Q}$ is uniformly distributed at the-outer surface of the ring. Thus, electric field inside the sphere is zero.
Then the positive charge of the ring will interact equally a charge placed at centre of ring will be in unstable equilibrium.
So the effect of electric field on charge q due to the positive charge $Q$ is zero.
Now, there are two forces are active between charges $(Q$ and q).
(i) attractive force. (ii) repulsive force.
There are two cases obtained :
Case I : When charge $q>0$ i.e., $q$ is a positive charge, there creates a repulsive force between charge $q$ and $Q$.
The repulsive forces of charge $Q$ from all around the charge $q$ will push it towards.ihe centre if it is displaced from the centre of the ring.
Case II : When charge $q < 0$ i.e., $q$ is a negative charge then there is an attractive force between charge $Q$ and $q$.
If $\mathrm{q}$ is displaced slightly small from the centre then the positive charges nearer to this charge will attract it towards itself and charge q will never return to the centre.
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