Max Charge on Sphere: Calculating with Electric Fields

[MrRandom66]

Homework Statement

An empty, hollow, spherical conductor with radius R = 20 cm is supported in air. Electrical breakdown occurs when the electric field at the conducting surface exceeds 3.0 × 10⁶ V m⁻¹.
What is the maximum charge that can be placed on the sphere?

Homework Equations

F = k (q/r^2)
F = Eq

The Attempt at a Solution

Trying to rearrange these to find q, however all I can get is something which cancels out q.

 

[berkeman]

Homework Statement

An empty, hollow, spherical conductor with radius R = 20 cm is supported in air. Electrical breakdown occurs when the electric field at the conducting surface exceeds 3.0 × 10⁶ V m⁻¹.
What is the maximum charge that can be placed on the sphere?

Homework Equations

F = k (q/r^2)
F = Eq

The Attempt at a Solution

Trying to rearrange these to find q, however all I can get is something which cancels out q.

I think there is something missing in the problem statement. The electric field has to be with respect to another conductor, placed some distance away (unless you can use infinity somehow). Is there anything else in the problem statement?

 

[MrRandom66]

I think there is something missing in the problem statement. The electric field has to be with respect to another conductor, placed some distance away (unless you can use infinity somehow). Is there anything else in the problem statement?

No, that's all.

 

[ehild]

You certainly learned that the electric field of a metal sphere is the same as if its whole charge concentrated in the centre.

Pretend that Q charge is in he centre of the sphere. What is the electric field at the surface of the sphere (R=20 cm)? ehild

 

[ehild]

Hi berkeman,

I think you meant electric potential, but it is electric field strength here.

ehild

 

[berkeman]

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