A small conducting sphere is hanged by an insulating thread between the plates of a parallel plate capacitor as shown in figure. The net force on the sphere is

Options

A. Towards plate A
B. Towards plate B
C. Upwards
D. Zero

Answer

To determine the net force on a small conducting sphere suspended between the plates of a parallel plate capacitor, we can follow these steps:

### Step 1: Understand the setup
We have a small conducting sphere hanging by an insulating thread between the plates of a parallel plate capacitor. The capacitor consists of two plates, one positively charged and the other negatively charged.

**Hint:** Visualize the arrangement of the capacitor and the sphere to understand the forces acting on it.

### Step 2: Identify the charges on the plates
Let’s denote the charge on the positive plate as \( +Q \) and the charge on the negative plate as \( -Q \). The charges on the plates are equal in magnitude but opposite in direction.

**Hint:** Remember that in a parallel plate capacitor, the charges on the plates are equal and opposite.

### Step 3: Determine the induced charge on the sphere
When the conducting sphere is placed in the electric field between the plates, it will experience induction. The charge on the sphere will be influenced by the electric field created by the plates.

- The charge induced on the side of the sphere facing the positive plate will be \( -Q' \) (negative).
- The charge induced on the side of the sphere facing the negative plate will be \( +Q' \) (positive).

**Hint:** Consider how the electric field affects the charges on the conducting sphere.

### Step 4: Calculate the net induced charge on the sphere
Since the charges induced on the sphere are equal in magnitude but opposite in sign, the net induced charge \( Q_{\text{net}} \) on the sphere will be:

\[ Q_{\text{net}} = -Q' + Q' = 0 \]

**Hint:** Remember that the net charge is the sum of all induced charges.

### Step 5: Determine the force on the sphere
The force \( F \) acting on the sphere due to the electric field \( E \) between the plates is given by:

\[ F = Q_{\text{net}} \cdot E \]

Since we found that \( Q_{\text{net}} = 0 \):

\[ F = 0 \cdot E = 0 \]

**Hint:** The force on a charge in an electric field is zero if the charge itself is zero.

### Step 6: Conclusion
The net force acting on the small conducting sphere is zero.

**Final Answer:** The net force on the sphere is \( 0 \).