A dipole of `2muC` charges each, consists of the positive charge at the point P (1, -1) and the negative charge is placed at the point Q(-1, 1). The work done in displacing a charge of `+1muC` from point `A(-3,-3)` to B (4, 4) is

Options

A. `1.6xx10^(-19)J`
B. `3.2xx10^(-19)J`
C. zero
D. `4.8 eV`

Answer

To solve the problem of finding the work done in displacing a charge of `+1μC` from point `A(-3,-3)` to point `B(4,4)` in the presence of a dipole with charges of `2μC` located at points `P(1, -1)` and `Q(-1, 1)`, we can follow these steps:

### Step 1: Understand the Configuration
We have a dipole consisting of a positive charge `+2μC` at point `P(1, -1)` and a negative charge `-2μC` at point `Q(-1, 1)`. The charge we are moving is `+1μC`, and we need to find the work done in moving this charge from point `A(-3, -3)` to point `B(4, 4)`.

**Hint:** Visualize the dipole and the points A and B on a coordinate plane to understand their relative positions.

### Step 2: Determine the Nature of the Path
The line connecting points A and B can be analyzed. The coordinates of A and B suggest that the path is straight. We need to check if this path intersects with the equatorial line of the dipole.

**Hint:** The equatorial line of a dipole is the line that is perpendicular to the dipole axis and passes through the midpoint of the dipole.

### Step 3: Find the Midpoint of the Dipole
The midpoint M of the dipole can be calculated as:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{1 + (-1)}{2}, \frac{-1 + 1}{2} \right) = (0, 0) \]

**Hint:** The midpoint is crucial for determining the equatorial line.

### Step 4: Determine the Equation of the Equatorial Line
The equatorial line of the dipole lies along the line that is perpendicular to the line joining the two charges. The line joining P and Q has a slope, and the perpendicular slope will give us the equation of the equatorial line.

**Hint:** Use the slope formula to find the slope of line PQ and then find the negative reciprocal for the equatorial line.

### Step 5: Check if Points A and B are on the Equatorial Line
The equation of the equatorial line can be derived from the coordinates of P and Q. Since the potential due to a dipole is zero along the equatorial line, we need to check if points A and B lie on this line.

**Hint:** Substitute the coordinates of A and B into the equation of the equatorial line to see if they satisfy it.

### Step 6: Calculate the Work Done
Since the potential along the equatorial line is zero, the potential at points A and B is also zero. The work done in moving a charge in an electric field is given by:
\[ W = q(V_B - V_A) \]
Since both \( V_A \) and \( V_B \) are zero:
\[ W = 1μC \times (0 - 0) = 0 \]

**Hint:** Remember that work done is related to the change in electric potential energy.

### Final Answer
The work done in displacing the charge of `+1μC` from point `A(-3, -3)` to point `B(4, 4)` is **0 Joules**.