Question #128540
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?
1
Expert's answer
2020-08-05T16:41:57-0400

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


E=σ2ε0E =\dfrac{\sigma}{2\varepsilon_0}

where ε0=8.85×1019F/m\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=σ12ε0σ22ε0=12ε0(σ1σ2)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=128.85×1019(4×10914×109)5.65×109V/mE = \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. 5.65×109V/m5.65\times 10^{9} V/m.


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