The work done to move a unit charge along an equipotential from `P` to `Q`

Options

A. must be defined as `-underset(P)overset(Q)intvecE.vec(dl)`
B. is zero
C. can have a non-zero value
D. both (a) and (b)are correct

Explanation

To solve the problem of finding the work done to move a unit charge along an equipotential surface from point P to point Q, we can follow these steps:

### Step 1: Understand the Concept of Equipotential Surfaces
Equipotential surfaces are surfaces where the electric potential is the same at every point. This means that if you move a charge along an equipotential surface, there is no change in electric potential energy.

**Hint:** Remember that electric potential (V) is constant along an equipotential surface.

### Step 2: Define Work Done in Moving a Charge
The work done (W) in moving a charge (Q) from point P to point Q in an electric field is given by the formula:
\[ W = Q(V_Q - V_P) \]
where \( V_Q \) is the potential at point Q and \( V_P \) is the potential at point P.

**Hint:** Work done depends on the change in potential energy, which is determined by the difference in electric potential.

### Step 3: Apply the Concept to the Given Problem
Since points P and Q are on the same equipotential surface, we have:
\[ V_P = V_Q \]
Thus, substituting this into the work done formula gives:
\[ W = Q(V_Q - V_P) = Q(0) = 0 \]

**Hint:** Since the potential difference is zero, the work done will also be zero.

### Step 4: Conclusion
For a unit charge (Q = 1), the work done to move it from point P to point Q along an equipotential surface is:
\[ W = 0 \]

### Final Answer
The work done to move a unit charge along an equipotential from P to Q is **0**.

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