Three identical, conducting plane parallel plates, each of areaAare held with equal separationdbetween successive surfaces. ChargesQ, 2Q,and3Qare placed on them. Neglecting edge effects. The sum of charges on the six surfaces is given bynQ. Find the value ofn.Correct answer is '3'. Can you explain this answer?

Question

Answer

Given:
- Three identical, conducting plane parallel plates
- Area of each plate: A
- Separation between plates: d
- Charges on the plates: Q, 2Q, and 3Q

To find:
- The value of n, which represents the sum of charges on the six surfaces

Solution:
Step 1: Understanding the situation
- We have three identical plates, each with an area A, separated by a distance d.
- The charges on the plates are Q, 2Q, and 3Q. Let's label these charges as Q1, Q2, and Q3, respectively.
- We need to find the sum of charges on all six surfaces, which is represented by nQ.

Step 2: Identifying the charges on each surface
- Let's consider the three plates one by one and determine the charges on each of their surfaces.

Plate 1:
- The charge on this plate is Q1 = Q.
- The surfaces of this plate are:
- Surface 1: Faces away from the other plates. It has a charge of Q1 = Q.
- Surface 2: Faces towards the second plate. It has a charge of -Q2 = -2Q.
- Surface 3: Faces towards the first plate. It also has a charge of -Q2 = -2Q.

Plate 2:
- The charge on this plate is Q2 = 2Q.
- The surfaces of this plate are:
- Surface 1: Faces towards the first plate. It has a charge of -Q2 = -2Q.
- Surface 2: Faces away from the first plate and towards the third plate. It has a charge of Q2 = 2Q.
- Surface 3: Faces towards the second plate. It also has a charge of -Q2 = -2Q.

Plate 3:
- The charge on this plate is Q3 = 3Q.
- The surfaces of this plate are:
- Surface 1: Faces towards the second plate. It has a charge of -Q3 = -3Q.
- Surface 2: Faces away from the second plate. It has a charge of Q3 = 3Q.
- Surface 3: Faces away from the other plates. It has a charge of Q3 = 3Q.

Step 3: Calculating the sum of charges on all surfaces
- Let's calculate the sum of charges on all six surfaces.

Surface 1:
- Charges on this surface: Q + (-2Q) + (-3Q) = -4Q

Surface 2:
- Charges on this surface: (-2Q) + 2Q + (-3Q) = -3Q

Surface 3:
- Charges on this surface: (-2Q) + (-2Q) + 3Q = -Q

Surface 4:
- Charges on this surface: Q + (-2Q) + 3Q = 2Q

Surface 5:
- Charges on this surface: (-2Q) + 2Q + 3Q =

Answer

The correct answer is: 3

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