Answer to Question #128540 in Physics for Ayman abuali

Question

Two infinite parallel plates one has a surface charge of density
4nC/m2 and the other has a surface charge 14nC/m2

. If the plates are
x meters apart, what is the electric field between the plates at a
distance x/4 from the leŌ plate?

Answer 1

The electric field of one infinite plate with a surface charge of density $\sigma$ is the following:

$$E =\dfrac{\sigma}{2\varepsilon_0}$$

where $\varepsilon_0 = 8.85\times10^{-19}F/m$ is  the vacuum permittivity. The electric field does not depend on particular point in space.

Since both plates are positively charged, then fields poduced by each plate at any point should be subtracted. The net field is:

$$E = \dfrac{\sigma_1}{2\varepsilon_0} - \dfrac{\sigma_2}{2\varepsilon_0} = \dfrac{1}{2\varepsilon_0}\left( \sigma_1 - \sigma_2\right)$$

Substituting numerical values, obtain:

$$E = \dfrac{1}{2\cdot 8.85\times10^{-19}}\left( 4\times 10^{-9} - 14\times 10^{-9}\right) \approx 5.65\times 10^{9} V/m$$

Answer. $5.65\times 10^{9} V/m$.