Understanding Induced Charges in an External Field

[harsh22902]

Homework Statement

In a conducting hollow sphere of inner and outer radii 5 cm and 10 cm, respectively, a point charge 1 C is placed at point A, that is 3 cm from the center C of the hollow sphere. An external uniform electric field to magnitude 20NC is also applied. Net electric force on this charge is 15 N, away from the center of the sphere as shown. Find the magnitude of net force exerted on the charge placed at point A by the induced charges on the sphere.

Relevant Equations

F=qE

Could'nt solve it

 

[harsh22902]

 

[kuruman]

Could'nt solve it

According to Forum rules (item 4) you need to show some effort at solving the problem before you can receive help. Please show us what you already know about such problems, what you tried so far and how you think you might approach this question.

 

[harsh22902]

According to Forum rules (item 4) you need to show some effort at solving the problem before you can receive help. Please show us what you already know about such problems, what you tried so far and how you think you might approach this question.

What I tried here is nothing mathematical. The charges in a cavity are sheilded from outside electric fields due to the conducting material. So what I could make out of it is that the forces acting on the charge myst be due to the induced charges on the internal cavity surface only and hence the final answer should be 15 Newtons. But it is mentioned in my textbook as 35 Newtons. Please help.

 

[Delta2]

What I tried here is nothing mathematical. The charges in a cavity are sheilded from outside electric fields due to the conducting material. So what I could make out of it is that the forces acting on the charge myst be due to the induced charges on the internal cavity surface only and hence the final answer should be 15 Newtons. But it is mentioned in my textbook as 35 Newtons. Please help.

What you say here appears to be correct and that's also what i was thinking but it is wrong if we think a bit more carefully. My hint for you here is this:
There are two "types" of induced charges in the metal sphere: one type are the induced charges from the induction from the point charge and the second type are the induced charges from the induction from the external E-field of 20N/C.

 

[harsh22902]

What you say here appears to be correct and that's also what i was thinking but it is wrong if we think a bit more carefully. My hint for you here is this:
There are two "types" of induced charges in the metal sphere: one type are the induced charges from the induction from the point charge and the second type are the induced charges from the induction from the external E-field of 20N/C.

I thought about it but what still appears confusing is how exactly will the induced charge due to the electric field exert a force on the charge within because for that we must have an idea about the distribution of induced charge(due to the field) on the outside and inside of the hollow sphere. But on searching further in some other textbook I found a solution which states that:
" External applied field's effect is neutralized by charge induced on outer surface, i.e., their combined effect is zero. Hence, force applied by induced charges on outer surface should be equal and opposite to that applied by electric field. This is equal to qE=1×20=20 N toward left. 15 N force is only due to induced charged on the inside surface of the hollow sphere. Hence, net force by induced charges is 15+20=35 N. "
Which still appears vague because here they are assuming that the external field is acting on the point charge and that is being neutralized by charge induced on the outer surface.

 

[Delta2]

...
Which still appears vague because here they are assuming that the external field is acting on the point charge and that is being neutralized by charge induced on the outer surface.

What exactly is vague? Yes the external field is acting on the point charge in the interior of the sphere. The shielding doesn't mean that the external field doesn't act, it means that its action is neutralized by the induced charges.

 

[harsh22902]

What exactly is vague? Yes the external field is acting on the point charge in the interior of the sphere. The shielding doesn't mean that the external field doesn't act, it means that its action is neutralized by the induced charges.

Okay so I think its clear to me now. What I was stuck on was the shielding part . Big conceptual error. Thanks! :D