Calculating Net Charge Using Electric Potential and Gauss' Law

In summary, to find the net charge on a spherical shell given the formula for electric potential V(r, theta), one can use Gauss' Law on a surface outside of the shell. This is because the electric field, which is the negative divergence of V, indicates the presence of a non-zero net charge. Alternatively, one can also find the magnitude of the charge by taking the electric field and applying Gauss' Law.
  • #1
azone
7
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If we are given the formula for the electric potential V(r,theta) outside a spherical shell, how can we find the net charge on the shell? Essentially, I guess I'm a little confused about the relationship between Electric Potential and Net Charge.

The way I thought about this is by finding the electric field, which is the negative divergence of V. And if there is an electric field, this must mean that there is a a net charge that is not zero. But how can I find the magnitude of the charge? Or is there an easier way that I'm missing?

thanks
 
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  • #2
Take your electric field and apply Gauss' Law to a surface outside of the shell.
 

1. What is electric potential?

Electric potential is a measure of the electric potential energy per unit charge at a specific point in an electric field.

2. How is electric potential different from electric charge?

Electric potential is a scalar quantity that describes the potential energy of a charge in an electric field, while electric charge is a fundamental property of matter that determines how it will interact with other charges.

3. How is electric potential calculated?

Electric potential can be calculated by dividing the electric potential energy by the charge at a specific point in an electric field.

4. What is the unit of electric potential?

The unit of electric potential is volts (V) in the International System of Units (SI).

5. How does electric potential affect the movement of charges?

Electric potential can influence the movement of charges as they will naturally move from areas of high potential to areas of low potential. The difference in potential between two points determines the strength and direction of the electric field and therefore affects the direction and speed of the charges' movement.

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