Question

The direction of electric field at a point just outside a positively charged spherical conductor is

Hint:

Electric field just outside ANY charged conductor is always perpendicular to its surface. For a sphere, perpendicular means radial. The sign of the charge dictates inward (-) or outward (+).

Answer 1

Step 1: Understanding the Concept:
In electrostatics, the surface of any conductor acts as an equipotential surface. This means there can be no potential difference between any two points on the surface, and consequently, no component of the electric field parallel to the surface.

Step 2: Key Formula or Approach:
The direction of the electric field $\mathbf{E}$ is related to the potential $V$ by $\mathbf{E} = -\nabla V$. Since the surface is equipotential, the gradient along the surface is zero. Therefore, the entire electric field vector must be perpendicular (normal) to the local surface.
Furthermore, electric field lines originate from positive charges and terminate on negative charges.

Step 3: Detailed Explanation:
1. Perpendicularity: Because the spherical conductor's surface is an equipotential surface, the electric field lines immediately outside it must be strictly perpendicular (normal) to the surface at every point.
2. Direction: The conductor is described as "positively charged". Electric field lines represent the direction of force on a positive test charge. A positive test charge placed outside the sphere would be repelled. Therefore, the field lines must point away from the surface.
Combining these two facts for a spherical geometry: lines perpendicular to a spherical surface point along the radius. Since they point away, the direction is defined as "radially outward".

Step 4: Final Answer:
The direction is radially outward.