A hemispherical shell is uniformly charge positively .the electric field at point on a diameter away from the centre is directed

Options

A. perpendicular to the diameter
B. parallel to the diameter
C. at an angle tilted towards the diameter
D. at an angle tilted away from the diameter

Explanation

To solve the problem of determining the direction of the electric field at a point on the diameter of a uniformly positively charged hemispherical shell, we can follow these steps:

### Step 1: Understand the Configuration
We have a hemispherical shell that is uniformly charged with positive charge. Visualize the shell as the upper half of a sphere, and we are interested in a point located on the diameter of this hemisphere, away from its center.

**Hint:** Visualize the hemispherical shell and the point on the diameter to understand the geometry involved.

### Step 2: Analyze the Electric Field Contribution
The electric field due to a positive charge is directed away from the charge. At any point on the diameter, the electric field contributions from different parts of the shell will vary based on their distance and angle relative to the point of interest.

**Hint:** Remember that electric field lines from positive charges always point away from the charge.

### Step 3: Consider Symmetry
Due to the symmetry of the hemispherical shell, for every small charge element on one side of the diameter, there is an equal charge element on the opposite side that contributes to the electric field at the point. The horizontal components (parallel to the diameter) of these electric fields will cancel each other out.

**Hint:** Use symmetry to simplify the problem. Components of the electric field that are equal and opposite will cancel.

### Step 4: Identify the Resultant Electric Field Direction
Since the horizontal components cancel, only the vertical components (perpendicular to the diameter) will add up. Thus, the resultant electric field at the point on the diameter will be directed away from the shell and perpendicular to the diameter.

**Hint:** Focus on the components of the electric field that do not cancel out; this will help you determine the net direction.

### Step 5: Conclusion
The electric field at the point on the diameter away from the center of the hemispherical shell is directed perpendicular to the diameter.

**Final Answer:** The electric field at a point on the diameter away from the center of the positively charged hemispherical shell is directed perpendicular to the diameter.