# Force on a charge from a line of uniform charge density

• lonely_coyote
In summary, the equation in vector component form for the force on a point charge located a distance d from a vertical rod with uniform charge density Q and length L on the 45o line that bisects the positive x and y axes would be Fx=1/(4πε0) x q0q(d/L)/√(d2+L2/4) and Fy=1/(4πε0) x q0q(d/L)/√(d2+L2/4). The equation for the force on the y-axis can also be determined using the same formula.
lonely_coyote

## Homework Statement

Write an equation in vector component form for the force when a point charge q0 is located a distance d from a vertical rod of uniform charge density Q and length L on the 45o line that bisects the positive x and y axes.

basically if you can picture a rod going vertically on the z axis, then halfway down the rod and a distance d away is a point that i need to find the force on

## Homework Equations

dF=1/(4$$\pi$$$$\epsilon$$0) x q0dq/r2
note that these equations are supposed to look like 4 x pi x epsilon 0, not for raised to that power

## The Attempt at a Solution

I have determined that the force were the charge to be locate on the y-axis would be
Fy=1/(4$$\pi$$$$\epsilon$$0) x q0q/(y x (y2 + L2/4)1/2)

but I am unsure of the equation for when it is on the 45o line. How would the equation change? Thanks in advance.

## 1. What is the equation for force on a charge from a line of uniform charge density?

The equation for force on a charge (q) from a line of uniform charge density (λ) is F = (k*q*λ)/r, where k is the Coulomb's constant and r is the distance between the charge and the line of charge.

## 2. How do you determine the direction of the force on a charge from a line of uniform charge density?

The direction of the force on a charge from a line of uniform charge density is determined by the right-hand rule. If you point your right thumb in the direction of the line of charge, the direction of the force on the charge will be perpendicular to your thumb and towards or away from the line depending on the charge of the particle.

## 3. Can the force on a charge from a line of uniform charge density be repulsive?

Yes, the force on a charge from a line of uniform charge density can be repulsive if the charge of the particle is the same as the charge density of the line. In this case, the force will be directed away from the line of charge.

## 4. How does the distance between the charge and the line of charge affect the force?

The force between a charge and a line of uniform charge density is inversely proportional to the square of the distance between them. This means that as the distance increases, the force decreases.

## 5. Is the force on a charge from a line of uniform charge density affected by the charge of the particle?

Yes, the force on a charge from a line of uniform charge density is directly proportional to the charge of the particle. This means that as the charge of the particle increases, the force also increases.

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