# Forces in electric fields

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## Forces in electric fields

**If field strength, E, is:**

In the case of a **uniform field** it's easy.

* Remember:*.

* Example*.

**If the charge in the diagram above is Q = -3 x 10 ^{-6} C, the pd across the plates is 100V and the plate separation is 1.5 cm, what's the force on charge Q?**

* Answer*.

* Note:* the direction is up towards the positive plate as it's a negative charge.

In **radial fields**, you find the force using F = Eq again except here, note that

so

* where*.

Q_{1} = one of the charges

Q_{2} = the other charge

ε = permittivity of the material, usually ε_{0}.

r = separation between the centres of the charges.

This is Coulomb's Law

**Let's look at another...**

* Example*.

**Whats the force on a charge of +2 x 10 ^{-6}C when it is 0.5 m from a charge of +3 x 10^{-6}C? (
= 9 x 10^{9} mF^{-1}).**

* Answer*.

A more complex situation exists if there are three or more charges in the field. In this case, only consider two of the charges at any one time, find the effect due to them, then consider the effect of the other charge and add the two answers at the end (with careful thought about sign).

* Example*.

**What's the force on B due to A and C?**

* Answer*.

Consider A-B first and ignore C.

to the right.

Now consider B-C and ignore A.

to the left.

So you have two forces in opposite directions. Find the resultant.

**Answer:****3.6x10 ^{10}N from A towards C.**

Be careful if the signs of the charges are different. For example.

Do you agree that the resultant force on B is zero here?

Do you agree that the resultant force on B has got to be to the right? Think about it!

* One last example...*.

**Find the point, x between these two charges, A and B, where the force on a +2C charge, C, is zero.**

* Answer*.

To solve this, the force on C due to A must be equal and opposite to the force on C due to B.

So F_{AC} = F_{BC}

To solve, we need to use the information that r_{AB} = 1- r_{BC},

So,

We can simplify, cancelling Q_{C} from each side of the equation and 4π ε_{o} from each side,

So,

Now put in thr changesm Q_{A}= + 4C, Q_{B} = + 1C and you only have one unknown r_{BC} and you should be able to work that out!

**(Can you get the r _{BC} = 0.33m?)**