NCERT Physics Class12 Exampler Chapter-2 Electrostatic Potential and Capacitance Part-7

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Q.22 Calculate potential energy of a point charge placed along the axis due to a charge uniformly distributed along a ring of radius . Sketch P. E. as a function of axial distance from the centre of the ring. Looking at graph, can you see what would happen if is displaced slightly from the centre of the ring (along the axis)?

Solution:

Image of Potential Energy Graph

Image of Potential Energy Graph

Image of Potential Energy Graph

Image of Potential Energy Variation Graph

Image of Potential Energy Variation Graph

Image of Potential Energy Variation Graph

  • The variation of potential energy with is shown in the figure.

  • The charge displaced would perform oscillations. We cannot conclude anything just by looking at the graph.

Q.23 Calculate potential on the axis of a ring due to charge uniformly distributed along the ring of radius .

Solution:

Long Type Answer

Q.24 Find the equation of the equipotentials for an infinite cylinder of radius , carrying charge of linear density .

Solution:

To find the potential at distance from the line consider the electric field. We note that from symmetry the field lines must be radially outward. Draw a cylindrical Gaussian surface of radius and length . Then

Image of Cylinder of Radius

Image of Cylinder of Radius

Image of Cylinder of Radius

Or,

So

Hence, if is the radius,

So,

For a given V,

So,

The equipotential surface are cylinders of radius