ABC is a right angle triangle AB = 3 cm, BC = 4 cm charge +15, +12, -12 esu are placed at A, B and C respectively. The magnitude of the force experienced by the charge at B in dyne is -

Options

A. 125
B. 35
C. 22
D. 0

Answer

To solve the problem, we need to calculate the net force experienced by the charge at point B due to the charges at points A and C in the right triangle ABC.

### Step-by-Step Solution:

1. **Identify the Charges and Their Positions:**
- Charge at A (Q_A) = +15 esu
- Charge at B (Q_B) = +12 esu
- Charge at C (Q_C) = -12 esu
- Distance AB = 3 cm
- Distance BC = 4 cm

2. **Calculate the Distance AC using Pythagorean Theorem:**
\[ AC = \sqrt{AB^2 + BC^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ cm} \]

3. **Calculate the Force on Charge B due to Charge A (F_AB):**
- The formula for the electrostatic force is given by Coulomb's Law:
\[ F = k \frac{|Q_1 Q_2|}{r^2} \]
- Here, \( k = 1 \) in cgs units, \( Q_1 = 15 \) esu, \( Q_2 = 12 \) esu, and \( r = 3 \) cm.
\[ F_{AB} = 1 \cdot \frac{15 \cdot 12}{3^2} = \frac{180}{9} = 20 \text{ dyne} \]
- Direction: Since both charges at A and B are positive, the force will be repulsive and directed to the left (negative x-direction).

4. **Calculate the Force on Charge B due to Charge C (F_BC):**
- Here, \( Q_1 = 12 \) esu, \( Q_2 = 12 \) esu, and \( r = 4 \) cm.
\[ F_{BC} = 1 \cdot \frac{12 \cdot 12}{4^2} = \frac{144}{16} = 9 \text{ dyne} \]
- Direction: Since charge B is positive and charge C is negative, the force will be attractive and directed upwards (positive y-direction).

5. **Determine the Net Force on Charge B:**
- The forces are perpendicular to each other:
\[ \vec{F}_{net} = F_{AB} \hat{i} + F_{BC} \hat{j} = -20 \hat{i} + 9 \hat{j} \]

6. **Calculate the Magnitude of the Net Force:**
\[ F_{net} = \sqrt{(-20)^2 + (9)^2} = \sqrt{400 + 81} = \sqrt{481} \]
- Approximating \( \sqrt{481} \):
\[ \sqrt{481} \approx 21.93 \text{ dyne} \approx 22 \text{ dyne} \]

### Final Answer:
The magnitude of the force experienced by the charge at B is approximately **22 dyne**.