# Electrostatic problem with vectors

• Niles
In summary, an electrostatic problem with vectors involves analyzing the behavior of electric charges using vector quantities such as electric fields, forces, and potentials. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. To calculate the electric field at a point due to multiple point charges, you can use the principle of superposition. The electric potential at a point is a measure of the potential energy per unit charge at that point and is represented by the symbol V or φ. The direction of an electric field at a point is important in determining the direction of the force that would act on a positive test charge placed at that point.

## Homework Statement

Hi all.

A uniformly charged sphere centeren at (0,0,0) has a spherical hole inside and the hole has it's center at (d,0,0). Find the electric field inside the hole.

## The Attempt at a Solution

I use superposition. The electric field from the sphere itself is trivial.

Now to find the electric field from the hole. This is also trivial, but the direction of E_x is not just x, but x-d. Am I correct about that?

Yes.

## What is an electrostatic problem with vectors?

An electrostatic problem with vectors involves analyzing the behavior of electric charges using vector quantities such as electric fields, forces, and potentials.

## What is the difference between scalar and vector quantities?

Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. Examples of scalar quantities include mass and temperature, while examples of vector quantities include velocity and force.

## How do you calculate the electric field at a point due to multiple point charges?

To calculate the electric field at a point due to multiple point charges, you can use the principle of superposition. This means that you calculate the electric field at the point for each individual charge, and then add them together vectorially to find the total electric field.

## What is the meaning of the term "electric potential"?

The electric potential at a point is a measure of the potential energy per unit charge at that point. It is a scalar quantity and is often represented by the symbol V or φ.

## What is the significance of the direction of an electric field?

The direction of an electric field at a point is the direction that a positive test charge would move if placed at that point. This direction is important in determining the direction of the force that would act on the test charge, as the force is in the same direction as the electric field.