A 0.50 gm ball carries a charge of magnitude `10mu C`. It is suspended by a string in a downward electric field of intensity 300N/C. If the charge on the ball is positive, then the tension in the string is `(g = 10 ms^(-2))`

Options

A. `5 xx 10^(-3)N`
B. `8 xx 10^(-3)N`
C. `2 xx 10^(-3)N`
D. zero

Answer

To solve the problem, we need to find the tension in the string when a charged ball is suspended in a downward electric field. Let's break it down step by step.

### Step 1: Identify the forces acting on the ball
The ball experiences two main forces:
1. Gravitational force (weight) acting downwards.
2. Electric force acting downwards due to the electric field.

### Step 2: Calculate the gravitational force (weight)
The weight (W) of the ball can be calculated using the formula:
\[ W = mg \]
where:
- \( m = 0.50 \, \text{g} = 0.50 \times 10^{-3} \, \text{kg} \)
- \( g = 10 \, \text{m/s}^2 \)

Calculating the weight:
\[ W = 0.50 \times 10^{-3} \, \text{kg} \times 10 \, \text{m/s}^2 = 5 \times 10^{-3} \, \text{N} \]

### Step 3: Calculate the electric force
The electric force (F_e) acting on the ball can be calculated using the formula:
\[ F_e = qE \]
where:
- \( q = 10 \, \mu C = 10 \times 10^{-6} \, C \)
- \( E = 300 \, \text{N/C} \)

Calculating the electric force:
\[ F_e = 10 \times 10^{-6} \, C \times 300 \, \text{N/C} = 3 \times 10^{-3} \, \text{N} \]

### Step 4: Determine the net force acting on the ball
Since both the gravitational force and the electric force are acting downwards, we can find the total force acting on the ball:
\[ F_{\text{total}} = F_e + W \]
\[ F_{\text{total}} = 3 \times 10^{-3} \, \text{N} + 5 \times 10^{-3} \, \text{N} = 8 \times 10^{-3} \, \text{N} \]

### Step 5: Calculate the tension in the string
The tension (T) in the string must balance the total downward force when the ball is in equilibrium. Therefore, the tension in the string is equal to the total downward force:
\[ T = F_{\text{total}} = 8 \times 10^{-3} \, \text{N} \]

### Final Answer
The tension in the string is \( 8 \times 10^{-3} \, \text{N} \).

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