Electric Field and Potential due to Induced Charges

[gracy]

Homework Statement

If there is an uncharged metal spherical body and a charge q outside it .Find Electric field due to induced charges.

Homework Equations

##E##=##\frac{Kq}{r^2}##

The Attempt at a Solution

If there is an uncharged metal spherical body and a charge q outside it then there will be induced charges on it's surface like this

Electric field inside the body should be zero.Electric field due to +q would be ##E##=##\frac{Kq}{r^2}## there fore Electric field due to induced charges should be equal in magnitude to that of ##E##=##\frac{Kq}{r^2}## and opposite in direction.But my question is this electric field due to induced charges is due to +q induced or -q induced?

 

[SammyS]

Homework Statement

If there is an uncharged metal spherical body and a charge q outside it .Find Electric field due to induced charges.

Homework Equations

##E##=##\frac{Kq}{r^2}##

The Attempt at a Solution

If there is an uncharged metal spherical body and a charge q outside it then there will be induced charges on it's surface like this
View attachment 93590
Electric field inside the body should be zero.Electric field due to +q would be ##E##=##\frac{Kq}{r^2}## there fore Electric field due to induced charges should be equal in magnitude to that of ##E##=##\frac{Kq}{r^2}## and opposite in direction.But my question is this electric field due to induced charges is due to +q induced or -q induced?

What does the question ask you to do? "Find Electric field due to induced charges." That must include all of the charges mentioned with the exception of the given charge, +q.

 

[gracy]

That must include all of the charges mentioned with the exception of the given charge, +q.

And what if we are asked to find electric field due to +q induced?

 

[SammyS]

And what if we are ask to find electric field due to +q induced?

The induced charge is distributed over the surface with varying density. It would be a very involved process to find the electric field due to +q_induced by itself or the electric field due to -q_induced by itself.