The electrostatic field due to a charged conductor just outside the conductor is

Options

A. Zero and paralel to the surface at every point inside the conductor
B. Zero and is normal to the surface at every point inside the conductor
C. Parallel to the surface at every point and zero inside the conductor
D. Normal to the surface at every point and zero inside the conductor.

Explanation

To find the electrostatic field due to a charged conductor just outside the conductor, we can follow these steps:

### Step 1: Understand the Concept of Electric Field and Potential
The electric field (E) and electric potential (V) are related through the equation:
\[ dV = -E \cdot dr \]
This means that the electric field is related to the change in potential over a small distance.

### Step 2: Recognize the Properties of Conductors
In electrostatics, the electric field inside a conductor is zero when it is in electrostatic equilibrium. This is because charges redistribute themselves on the surface of the conductor, leading to no electric field inside.

### Step 3: Analyze the Potential on the Surface of the Conductor
The potential on the surface of a charged conductor is constant. For a spherical conductor with charge \( Q \), the potential \( V \) at a distance \( r \) from the center is given by:
\[ V = \frac{kQ}{r} \]
where \( k \) is Coulomb's constant.

### Step 4: Determine the Change in Potential
Since the potential is constant on the surface of the conductor, the change in potential \( dV \) at the surface is zero:
\[ dV = 0 \]

### Step 5: Relate Change in Potential to Electric Field
From the equation \( dV = -E \cdot dr \), if \( dV = 0 \), it implies:
\[ E \cdot dr = 0 \]
This indicates that the angle \( \theta \) between the electric field and the displacement \( dr \) is 90 degrees (cosine of 90 degrees is zero).

### Step 6: Conclude the Direction of the Electric Field
Since the electric field is perpendicular to the surface of the conductor, we can conclude that:
- Just outside the conductor, the electric field lines are normal (perpendicular) to the surface of the conductor.

### Step 7: Final Statement
Thus, the electrostatic field due to a charged conductor just outside the conductor is directed normal to the surface of the conductor.

### Summary
The electrostatic field just outside a charged conductor is perpendicular to its surface.

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