Image confusion(electrostatics)

[Kolahal Bhattacharya]

Sir, when I was carrying out an image problem in electrostatics(a charge is kept near a grounded conducting sphere;we are to find the ratio of induced charges on the front face and on the rear one).The ratio comes positive.It seems to be correct as it matches with a teacher's comment.But I am thinking it should be negative.Because front face is induced with charge opposite to source charge,but the rear face is induced with the same type of charge as the source. Please help!

 

[andrevdh]

Why would there be any resultant charge on the rear of the sphere when it is grounded? What electrostatic force would hold this unbalanced charge there? If the sphere were not grounded one would naturally find the opposite charge on the rear of the sphere.

 

[kyle8921]

First of all, it is important to understand the concept of image charges in electrostatics. When a charge is placed near a grounded conducting sphere, it induces opposite charges on the surface of the sphere, creating an electric field that cancels out the electric field of the source charge. This is known as the method of images.

In this scenario, the charge on the front face of the sphere will be opposite in sign to the source charge, while the charge on the rear face will be of the same sign as the source charge. This is because the front face is closer to the source charge and experiences a stronger electric field, while the rear face is farther away and experiences a weaker electric field.

Now, coming to the issue of the ratio of induced charges on the front and rear faces, it is important to note that both of these charges will be positive. This is because the induced charges are not the same as the source charge, but rather a result of the electric field created by the source charge. The magnitude of these induced charges may be different, but the sign will always be positive.

Therefore, the ratio of induced charges on the front and rear faces will be positive, which is consistent with your teacher's comment. It is important to remember that the sign of the induced charges is not determined by the type of charge on the source, but rather the direction of the electric field created by the source.

I hope this explanation helps clear up any confusion. If you still have doubts, I would suggest consulting with your teacher or referring to a textbook for further clarification. Electrostatics can be a complex topic, so it is always helpful to seek guidance from reliable sources.