Friday 26 June 2020

homework and exercises - Force on the central charge


While solving some exercise questions of electrostatics, I come across a problem given in the image:



enter image description here


Also what will the force on central charge only due to the shell?


I thought that there is already a charge $Q$ which is uniformly distributed on surface and due to charge $q1$ shell surface may aquire some induced charge and the net charge on surface will be sum of that induced charge and charge $Q$ and this may be non-uniformly distributed on the outer surface of shell. But whatever be the charge on outer surface, there will be a charge of equal magnitude but opposite sign on the inner surface which will be uniformly distributed over inner surface. So net force from these charges on the central charge $q$ will be zero.


But it was given in solution that force on charge $q$ due to both shell & charge outside is zero but only due to the shell was towards right. If we consider only the shell neglecting $q1$, then also the charge $-Q$ will be uniformly distributed on inner walls and will exert net force zero. Then why rightward? Is there anything which I am assuming wrong?



Answer



No, in the presence of the point charge $q_1$, the shell will no longer be uniformly charged: it will change its distribution so as to keep the electric field inside the shell zero. This is what the charge distribution will look like:


enter image description here


So the sum of the electric field due to both the shell and $q_1=0$. The force on the charge at the center is zero. The force due to $q_1$alone is $\frac{kqq_1}{r^2}$ to the left so the force due to he shell alone must have the same magnitude and be directed to the right. Whe they say "consider only the shell neglecting $q_1$" they mean find the force due to the shell alone in the same scenario, not to forget that $q_1$ is there at all, and the effect its presence has.


No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...