Welcome back, students. So, students in previous module we had just mentioned potential due to various continuous charges. We learnt potential due to ring of charge, due to an arc of charge. More over we also talked about potential due to a line of charge. Now, let us extend the discussion and study potential due to spherical charge configurations.

So, let us start with hollow spherical charge. Let us say we have a hollow sphere whose charge is capital Q and radius is capital R. Now, what will be potential at any point inside, say at a distance r from the centre? Students, potential at any point inside as a matter of fact is k capital Q by capital R. It is constant, it is independent of small r, right, surprised. So remember students, potential inside a hollow spherical charge distribution is constant, it is same as that of potential at surface. So, if we draw the graph of potential versus R for inside the region it will be a constant. So, till r small r does not become capital R, potential will be a constant, as shown. Now, what will be potential at any point on the outside? So, at any point on outside potential will be equal to k capital Q by small r. So, its graph will be a hyperbolic graph as shown which will be inversely proportional to small r. Students, I hope you remember what was electric field due to hollow spherical charge distributions. Electric field outside was kQ by small r square and inside it was zero. So, we had learned that for outside points the sphere of charge behaves like a point charge placed at centre. The story remains the same even for potentials. But for inside electric field inside was zero and here electric inside it is k capital Q by capital R that is constant.

Now, let’s talk about solid spherical charge distributions. Again let us consider we have solid sphere having charge capital Q and radius r. Now, what will be potential at a small r distance inside the solid sphere, will it be constant like the case of hollow spheres? No, students, it will not be constant. It will be equal to some (2:39) some tough complicated formula but quite easy to remember. k capital Q by 2 capital R into 3 minus small r square by capital R square. It is very big complicated formula but still not that tough to remember. Remember, repeat it 3 times with me, potential inside a solid spherical charge distribution is k capital Q by 2 capital R into 3 minus small r square by capital R square. Two more times, potential inside due to solid spherical charge distribution is k capital Q by 2 capital R into 3 minus small r square by capital R square. Third time, potential inside due to solid spherical charge distribution is k capital Q by 2 capital R into 3 minus small r square by capital R square. Students, you please repeat it, I will have to move on but you can repeat it as many times as you want. Now, if you have to draw the graph of this potential. You can see in this case, potential is a quadratic function, it is proportional to minus r square. So, its graph will be something like this. Potential at o will be basically potential at centre having small r is equal to zero. So, it will be 3kQ by 2R and potential at surface will be at small r is equal to capital R it will be equal to k capital Q by R. So, potential inside is, we are aware of, what will be potential outside. Now, at outside point potential just like hollow spherical charges, potential is constant, is like potential at centre. Its capital KQ by small r. So, at outside points potential due to the solid sphere is same as that of potential due to a point charged placed at centre. It will be equal to k capital Q by small r. So, if you have to draw the graph it will again be a hyperbolic function. So, students, I hope you remember potential due to hollow sphere inside is constant, due to solid sphere inside is this, tough, this big formula. Potential outside due to hollow sphere and solid sphere is same.

We will get back in next module. You please repeat this module as these particular formulas are important. Till then thank you, students.