Question

Two identical, infinite conducting plates are kept parallel to each other and are separated by a distance \( d \). The uniform charge densities on the plates are \( +\sigma \) and \( -\sigma \). The electric field at a point between the two plates is \( E = n \left( \frac{\sigma}{\epsilon_0} \right) \), where \( n \) is ........

Hint:

For two parallel conducting plates with opposite charge densities, the electric field between them is the sum of the fields from each plate.

Answer 1

Correct Answer: 2

Step 1: Understanding the electric field between conducting plates.
For two infinite conducting plates with opposite charge densities \( +\sigma \) and \( -\sigma \), the electric field between them is given by: \[ E = \frac{\sigma}{\epsilon_0} \] This is the field produced by one plate. Since both plates contribute to the electric field, the total electric field between them is twice this value. Hence, the total electric field is: \[ E = 2 \times \frac{\sigma}{\epsilon_0} \] Step 2: Conclusion.
The value of \( n \) is 2.