Question:
Three infinite charged sheets are placed parallel. Find electric field at point \(P\).
Three infinite charged sheets are placed parallel. Find electric field at point \(P\).
Show Hint
Each sheet contributes \(\sigma/2\varepsilon_0\), just track direction carefully.
Updated On: Apr 23, 2026
- \(-\frac{4\sigma}{\varepsilon_0}\hat{k}\)
- \(\frac{4\sigma}{\varepsilon_0}\hat{k}\)
- \(-\frac{2\sigma}{\varepsilon_0}\hat{k}\)
- \(\frac{2\sigma}{\varepsilon_0}\hat{k}\)
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The Correct Option is C
Solution and Explanation
Concept:
Electric field due to infinite sheet:
\[
E = \frac{\sigma}{2\varepsilon_0}
\]
Direction:
• Away from \(+\sigma\)
• Towards \(-\sigma\)
Step 1: Identify sheets
Top: \(+3\sigma\)
Middle: \(-2\sigma\)
Bottom: \(-\sigma\)
Step 2: Field contributions at \(P\)
From \(+3\sigma\): downward \[ E_1 = \frac{3\sigma}{2\varepsilon_0} \] From \(-2\sigma\): upward \[ E_2 = \frac{2\sigma}{2\varepsilon_0} \] From \(-\sigma\): upward \[ E_3 = \frac{\sigma}{2\varepsilon_0} \]
Step 3: Net field
\[ E = \frac{3\sigma}{2\varepsilon_0} - \frac{3\sigma}{2\varepsilon_0} = -\frac{2\sigma}{\varepsilon_0}\hat{k} \] Conclusion: \[ -\frac{2\sigma}{\varepsilon_0}\hat{k} \]
• Away from \(+\sigma\)
• Towards \(-\sigma\)
Step 1: Identify sheets
Top: \(+3\sigma\)
Middle: \(-2\sigma\)
Bottom: \(-\sigma\)
Step 2: Field contributions at \(P\)
From \(+3\sigma\): downward \[ E_1 = \frac{3\sigma}{2\varepsilon_0} \] From \(-2\sigma\): upward \[ E_2 = \frac{2\sigma}{2\varepsilon_0} \] From \(-\sigma\): upward \[ E_3 = \frac{\sigma}{2\varepsilon_0} \]
Step 3: Net field
\[ E = \frac{3\sigma}{2\varepsilon_0} - \frac{3\sigma}{2\varepsilon_0} = -\frac{2\sigma}{\varepsilon_0}\hat{k} \] Conclusion: \[ -\frac{2\sigma}{\varepsilon_0}\hat{k} \]
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