Electrostatics potential questions

[Mrudul Agrawal]

What should be the potential of a cube at infinity having 6 equal charges placed at its corners?In first attempt I made it zero as looking from infinity all tge 8 pt. charges will seem to be coincided at a single point and potential of a 8q charge at infinity would be zero..?

 

[Paul Colby]

The gradient of the electrostatic potential is the force per unit charge which will act on a 9th additional test charge in the neighborhood of the 8 corner charges. At a long distance from the 8 fixed charges this force will look like the force produced by a single charge 8Q. Since adding a constant to the potential doesn't change the gradient, you are free to make infinity 0 potential.

PS a cube has 8, not 6 corners.

 

[Mrudul Agrawal]

The gradient of the electrostatic potential is the force per unit charge which will act on a 9th additional test charge in the neighborhood of the 8 corner charges. At a long distance from the 8 fixed charges this force will look like the force produced by a single charge 8Q. Since adding a constant to the potential doesn't change the gradient, you are free to make infinity 0 potential.

Actually the question is that how much work is reqd. to takr a negative charge from the centre of this cube to infinity.
Then answer should be zero as the potential difference between centre and infinity pt. Is zero. But the ans is NOT ZERO

 

[Paul Colby]

Okay the question should be "what is the potential energy of a cube of 8 charges", not what is the electrostatic potential caused by 8 charges. You seek the energy it takes to construct the cube. This is just the sum of mutual potential energy of of all 8*7/2 = 24 pairs.

$E = \sum^8_{i<j} \frac{q_i q_j}{|r_i - r_j|}$

 

[Mrudul Agrawal]

Okay the question should be "what is the potential energy of a cube of 8 charges", not what is the electrostatic potential caused by 8 charges. You seek the energy it takes to construct the cube. This is just the mutual potential energy of of all 8*7/2 = 24 pairs.

I must send you the question then
Question no. 7

 

[Paul Colby]

Got it. I don't know what's going on with the carrying $-q$ from it's corner means. If they had written $q$ instead the answer would be the sum of the 7 mutual potentials between the moved charge and the remaining fixed charges.

PSSS I don't read sideways. I have a hard enough time with normal text. I missed the -q in the middle somehow.

 

[Paul Colby]

Bottom line is the potential of a charge is the sum of all the mutual potentials with other charges. In your case this is 8 corner charges wrt the center charge.

 

[Mrudul Agrawal]

Kk thanks