How Does a Charge Outside a Conducting Cube Affect Its Internal Electric Field?

[sankalpmittal]

Homework Statement

A positive charge q is placed in front of a conducting solid cube at a distance d from its centre. Find the electric field at the centre of the cube due to the charges appearing on its surface.

Homework Equations

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The Attempt at a Solution

A positive charge will induce charge -q and +q respectively at the opposite faces of the cube. But since the electric field inside a conductor is zero, the answer should be zero as the cube is a conductor. But its not ! How ?

Please help !

Thanks in advance... :)

 

[ehild]

The electric field due to surface charges cancels the electric field due to the charge q.

ehild

 

[sankalpmittal]

The electric field due to surface charges cancels the electric field due to the charge q.

ehild

Ok thanks ! I got the correct answer. However one more question: Is it not the universal case that electric field inside a charged conductor is zero ? Its non zero in this case because somehow field created by electron drift does not nullify the electric field due charge q ?

The answer says net electric field is towards charge q. Why ?

 

[ehild]

The static electric field inside a conductor is zero. Here you apply the principle of superposition: The net field is the sum of contributions of all charges or charge distributions. This way, the field due to the surface charges + the field of q = 0

ehild

 

[sankalpmittal]

The static electric field inside a conductor is zero. Here you apply the principle of superposition: The net field is the sum of contributions of all charges or charge distributions. This way, the field due to the surface charges + the field of q = 0

ehild

Ok but I understand this. Concentrating centre of cube, and drawing a Gaussian surface over there, it can be seen that net field is zero as all the charges reside outside that Gaussian surface. Again, how is the direction of electric field towards the charge +q ?

 

[ehild]

The net field is zero. Zero is the difference of two equal and opposite fields.

The method of superposition considers charge distributions in vacuum. There is no conducting cube, only some charge distribution along the planes where the faces of cube were. And apply Coulomb's law. That gives the field of charge q at the point where the centre of cube was. The contribution of the other charges must be the same, with opposite sign.

ehild

 

[sankalpmittal]

The net field is zero. Zero is the difference of two equal and opposite fields.

The method of superposition considers charge distributions in vacuum. There is no conducting cube, only some charge distribution along the planes where the faces of cube were. And apply Coulomb's law. That gives the field of charge q at the point where the centre of cube was. The contribution of the other charges must be the same, with opposite sign.

ehild

Ok, so there is the charge q placed near the face of the cube. It induces in the near face, charge -q and in the opposite face, charge q. Now the role of charge q outside is finished. Field due to one face is E and due to other face is -E. Hence net field due to surface charges is zero. How is it a non zero value and that too towards +q charge ?

 

[ehild]

There are field lines originated from the positive surface charges and ending in the negative ones. The field lines are normal to the faces of the cube. The net field of the surface charges at the centre of the cube is towards q.

ehild

 

[sankalpmittal]

There are field lines originated from the positive surface charges and ending in the negative ones. The field lines are normal to the faces of the cube. The net field of the surface charges at the centre of the cube is towards q.

ehild

Ok, so that means that the net field inside the cubical conductor is a non zero value and is directed towards +q charge. It is not coming zero, even by the superposition principle. How ?

And what do you mean by static field ? A field is just the hypothetical lines of electric force.

Thanks...

 

[ehild]

The electric field is zero inside the conducting cube. The contribution due to the free charge q is not, neither is that due to the induced surface charges. But these two contributions just cancel each other. In the picture, only the field lines due to the induced charges are shown.ehild

 

[sankalpmittal]

The electric field is zero inside the conducting cube. The contribution due to the free charge q is not, neither is that due to the induced surface charges. But these two contributions just cancel each other. In the picture, only the field lines due to the induced charges are shown.


ehild

Ok got it ! Thanks a lot, ehild !