# Force on a charge due to charged sheet

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1. Mar 31, 2016

### Yashbhatt

1. The problem statement, all variables and given/known data
I want to find the force on a positive charge placed at a distance $d$ from a positively charged infinite plate. Of course, it can be simply done by finding the electric field due to the plate using Gauss's Law.

But my teacher suggested a different method and I am unable to comprehend it. He said that the field lines due to this particular configuration would be the same as the one in which a negative charge were to be placed on the opposite side of the plate at a distance $d$ forming a dipole.

Here $d = d_1$.

2. Relevant equations
$$F=\frac{kq_1q_2}{r^2}$$
$$E=\frac{\rho}{2\epsilon_0}$$
$$\ \ \ \oint _S \vec{E} \cdot \vec{dA} = \frac{Q_{enclosed}}{\epsilon_0}$$
$$F=qE$$

3. The attempt at a solution
The normal electric field is $\frac{\rho}{2\epsilon_0}$ which gives a force independent from $d$ but using the above method, the force is $\frac{kQ^2}{(2d)^2}$ which depends on $d$ . What is the method at work? Is the force now simply the force between two positive and negative charges? i.e. Is the force on $+Q$ just $\frac{kQ^2}{(2d)^2}$ ?

2. Mar 31, 2016

### ehild

Copy the original text of the problem, please.
You said that the infinite plate was positively charged. Was the plate metal or insulator? What was the surface charge density on it?

3. Mar 31, 2016

### Yashbhatt

The plate is a metal plate and the surface charge density is $\rho$.