Question

Two large, thin, parallel sheets have surface charge densities of opposite signs and equal magnitude \(\sigma\). What is the magnitude of the electric field \((E)\) in the region between the sheets?

• A. \(\dfrac{\sigma}{2\varepsilon_{0}}\)
• B. \(\dfrac{\sigma}{\varepsilon_{0}}\)
• C. Zero
• D. \(\dfrac{2\sigma}{\varepsilon_{0}}\)

Hint:

Remember the electric field due to an infinite charged sheet: \[ \boxed{E=\frac{\sigma}{2\varepsilon_{0}}} \] For two parallel sheets having equal and opposite charges, \[ \boxed{ E_{\text{between}} = \frac{\sigma}{\varepsilon_{0}} } \] while \[ \boxed{ E_{\text{outside}}=0. } \]

Answer 1

The Correct Option is B

Each infinite sheet produces a field of magnitude $\sigma/(2\varepsilon_0)$ on either side. Between two sheets carrying opposite surface charge densities $+\sigma$ and $-\sigma$, the individual fields point in the same direction and add, giving $E_{total} = \sigma/\varepsilon_0$.