Force on charges separated by grounded spherical condcutor

In summary, the force on the right charge in a grounded conductive spherical shell with radius R, where a charge is held at d and (-d) with d>R, is affected by the presence of the conductive sphere and can be calculated using the equation F=q*q/r^2, taking into account the effects of the sphere on the charges.
  • #1
Leah_Sh
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Homework Statement


Grounded conductive spherical shell is given. Radius R. Charge is held in d and (-d).
d>R. as in the pic.
What is the force on the right charge?

Homework Equations


F=q*q/r^2


The Attempt at a Solution


I thought it's just F=(q^2)/(4d^2).
Why it's wrong?
the right answer is marked.
Tnx.
 

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  • #2


Your suggestion would be correct if there were no conductive sphere there. However, the sphere has some effects. The presence of the positive charge to the right will electrostatically pull some negative charge to the rightmost surface of the sphere, and similarly on the leftmost surface of the sphere (except opposite polarity). That is the source of the extra terms at a distance of d-R and d+R respectively.

That said, I am unsure about the final expression, it doesn't quite seem dimensionally consistent but it is the only answer which seems to have charges in the right spots with the right polarities.
 

FAQ: Force on charges separated by grounded spherical condcutor

How is the force between charged particles calculated on a grounded spherical conductor?

The force between charged particles on a grounded spherical conductor is calculated using Coulomb's Law. This law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Can the force between charged particles on a grounded spherical conductor be repulsive?

Yes, the force between charged particles on a grounded spherical conductor can be repulsive. This is because like charges repel each other, and the charges on a grounded spherical conductor can redistribute themselves to create repulsive forces.

Does the size of the conductor affect the force between charged particles?

Yes, the size of the conductor does affect the force between charged particles. A larger conductor will have a greater surface area, allowing for more charge to accumulate and therefore resulting in a stronger force between charged particles.

How does grounding affect the force between charged particles on a spherical conductor?

Grounding a spherical conductor allows for the redistribution of excess charge, which can affect the force between charged particles. This can result in a decrease in the force as the charges become more evenly distributed.

Is the force between charged particles on a grounded spherical conductor affected by the charge of the particles?

Yes, the force between charged particles on a grounded spherical conductor is affected by the charge of the particles. As mentioned before, Coulomb's Law states that the force is directly proportional to the product of the charges, so an increase in the charge of either particle will result in a stronger force between them.

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