I have a few questions pertaining to some concepts in electrostatics, I'd be grateful if someone would help me out.
1) When we place a positive point charge inside a hollow conducting sphere, at its center, field lines emerge uniformly from the sphere. Okay, easy enough. Now, if we place the point charge inside the hollow sphere at a point other than the center, negative charge is induced on the inner surface of the sphere and equal amount of positive charge on its outer surface, now field lines inside the sphere are distorted i.e in a diagram we represent more closely spaced field lines where the charge is closer to the surface of the sphere than at points where it is relatively farther. So far so good. But when the lines emerge from the sphere they emerge out uniformly just as if the charge was at the center. How does that happen? An explanation I found said that the induced negative charge does not produce a field so they emerge uniformly. That just went over my head. I'd appreciate it if someone could explain why to me, explain like you would to a toddler XD
2)How can you transfer complete charge from a charged conductor to a neutral one? (Same sign charge)
Edit - Use of induction to create polarization of charge (charge of the neutral body opposite in sign to that of the charged body collects around the side closer to the charged body and the similar charges get repelled to the other side of the neutral body. So one side of the body has partial positive charge and the other side has equal partial negative charge, so the body still remains electrically neutral) and then earthing it will obviously not work.
But if I connect the bodies with a conducting wire, only half of the charge will be transferred ....
Is there any other way?
3) If I place a conductor in a uniform electric field and then cut out a cavity in the conductor, will the electric field exist in the cavity? I remember reading somewhere that it doesn't but why not? I consulted a lot of books but most of them simply stated this or said that it can be proved by the use of higher mathematics :P
4) Using Gauss law if we get enclosed charge = 0, does it necessarily imply that electric field is also 0 inside the body? And is the field under consideration internal (caused by the charge inside the body) or external (by other charges existing outside the Gaussian surface)? So will external field exist inside the Gaussian surface even if charge enclosed is 0?
Edit - Okay so the electric field under consideration is both internal and external. So q being 0 in Gauss's law implies that the number of field lines entering is equal to the number of field lines leaving the body? And also since according to Gauss law the net charge enclosed is proportional to the dot product of E(vector) and ds(vector) so it merely implies that the angle between the area vector and field vector is 90? So that doesn't mean field doesn't exist? Are my speculations correct?
And also, shouldn't a Gaussian surface necessarily be an equipotential (potential same at all points on the surface) surface? Any supporting or contradictory examples with the explanation would be helpful
5) If you take a uniformly charged (volume charge) sphere and consider a concentric smaller sphere inside the bigger sphere then what kind of field lines emerge from the smaller sphere and why? Will the charge outside the smaller sphere affect the field lines emerging? (I know field lines are imaginary but how will I draw them in this case?
6) How do I go about calculating electric potential at the center or corner of a uniformly charged (volume charge) cube? I mean the field emerging will be non-uniform right? And my friend told me I can't use Gauss's law .... I only know that V=kq/r and rho=q/(side)cube
7) When we place a point charge at the corner of a cube, we take 1/8 part of it to be inside the cube and when we place it on a face, we take 1/2 part to be inside. That is understandable with a sphere but a point charge is a .... point! So how do we start considering it like a sphere and making it into parts?
8) I'd like it if someone could show me what a non-uniform field looks like and what kind of body it emerges from. I couldn't find it in any of my reference books and googling it turned out to be an epic fail
I'd appreciate it if any existing conceptual mistakes in my explanations are pointed and any misconception I may be having cleared.
Thank you to anyone who takes the time to explain :)
PS - I really hope this isn't considered a homework question because I have problems with the concepts. Reason for not mentioning book names - They're books by Indian authors not sold internationally
1) When we place a positive point charge inside a hollow conducting sphere, at its center, field lines emerge uniformly from the sphere. Okay, easy enough. Now, if we place the point charge inside the hollow sphere at a point other than the center, negative charge is induced on the inner surface of the sphere and equal amount of positive charge on its outer surface, now field lines inside the sphere are distorted i.e in a diagram we represent more closely spaced field lines where the charge is closer to the surface of the sphere than at points where it is relatively farther. So far so good. But when the lines emerge from the sphere they emerge out uniformly just as if the charge was at the center. How does that happen? An explanation I found said that the induced negative charge does not produce a field so they emerge uniformly. That just went over my head. I'd appreciate it if someone could explain why to me, explain like you would to a toddler XD
2)How can you transfer complete charge from a charged conductor to a neutral one? (Same sign charge)
Edit - Use of induction to create polarization of charge (charge of the neutral body opposite in sign to that of the charged body collects around the side closer to the charged body and the similar charges get repelled to the other side of the neutral body. So one side of the body has partial positive charge and the other side has equal partial negative charge, so the body still remains electrically neutral) and then earthing it will obviously not work.
But if I connect the bodies with a conducting wire, only half of the charge will be transferred ....
Is there any other way?
3) If I place a conductor in a uniform electric field and then cut out a cavity in the conductor, will the electric field exist in the cavity? I remember reading somewhere that it doesn't but why not? I consulted a lot of books but most of them simply stated this or said that it can be proved by the use of higher mathematics :P
4) Using Gauss law if we get enclosed charge = 0, does it necessarily imply that electric field is also 0 inside the body? And is the field under consideration internal (caused by the charge inside the body) or external (by other charges existing outside the Gaussian surface)? So will external field exist inside the Gaussian surface even if charge enclosed is 0?
Edit - Okay so the electric field under consideration is both internal and external. So q being 0 in Gauss's law implies that the number of field lines entering is equal to the number of field lines leaving the body? And also since according to Gauss law the net charge enclosed is proportional to the dot product of E(vector) and ds(vector) so it merely implies that the angle between the area vector and field vector is 90? So that doesn't mean field doesn't exist? Are my speculations correct?
And also, shouldn't a Gaussian surface necessarily be an equipotential (potential same at all points on the surface) surface? Any supporting or contradictory examples with the explanation would be helpful
5) If you take a uniformly charged (volume charge) sphere and consider a concentric smaller sphere inside the bigger sphere then what kind of field lines emerge from the smaller sphere and why? Will the charge outside the smaller sphere affect the field lines emerging? (I know field lines are imaginary but how will I draw them in this case?
6) How do I go about calculating electric potential at the center or corner of a uniformly charged (volume charge) cube? I mean the field emerging will be non-uniform right? And my friend told me I can't use Gauss's law .... I only know that V=kq/r and rho=q/(side)cube
7) When we place a point charge at the corner of a cube, we take 1/8 part of it to be inside the cube and when we place it on a face, we take 1/2 part to be inside. That is understandable with a sphere but a point charge is a .... point! So how do we start considering it like a sphere and making it into parts?
8) I'd like it if someone could show me what a non-uniform field looks like and what kind of body it emerges from. I couldn't find it in any of my reference books and googling it turned out to be an epic fail
I'd appreciate it if any existing conceptual mistakes in my explanations are pointed and any misconception I may be having cleared.
Thank you to anyone who takes the time to explain :)
PS - I really hope this isn't considered a homework question because I have problems with the concepts. Reason for not mentioning book names - They're books by Indian authors not sold internationally