Just outside a sharp point on a conductor , we will have , a larger ______ than just outside gradually curving places on the conductor.

Options

A. Electric field
B. Potential
C. Both (1) and (2)
D. None of these

Answer

To solve the question, we need to understand the relationship between the shape of a conductor and the electric field just outside its surface.

### Step-by-Step Solution:

1. **Understanding the Conductor's Shape:**
- Consider a conductor with various shapes, specifically focusing on a sharp point and a gradually curving area. The sharp point is denoted as point P, and the gradually curving area is denoted as point Q.

2. **Electric Field and Potential:**
- The electric potential (V) is the same across the surface of a conductor in electrostatic equilibrium. Thus, \( V_P = V_Q \) where \( V_P \) is the potential at point P and \( V_Q \) is the potential at point Q.

3. **Electric Field Relation:**
- The electric field (E) just outside the surface of a conductor is related to the surface charge density (σ) and the radius of curvature (R) of the surface. The formula for the electric field near a charged conductor is given by:
\[ E = \frac{\sigma}{\epsilon_0} \]
- For a point charge, the electric field can also be expressed as:
\[ E = \frac{KQ}{R^2} \]
- Here, K is a constant, Q is the charge, and R is the radius of curvature.

4. **Comparing Electric Fields:**
- At point P (the sharp point), the radius of curvature (R) is smaller than at point Q (the gradually curving area). Since the electric field is inversely proportional to the radius of curvature, we have:
\[ E_P > E_Q \]
- This means that the electric field just outside the sharp point (P) is larger than that just outside the gradually curving area (Q).

5. **Conclusion:**
- Therefore, just outside a sharp point on a conductor, we will have a larger electric field than just outside gradually curving places on the conductor.

### Final Answer:
Just outside a sharp point on a conductor, we will have a larger **electric field** than just outside gradually curving places on the conductor.