A small sphere of mass `m = 0.6 kg` carrying a positive charge `q = 80 muC` is connected with a light, flexible, and inextensible string of length `r = 30 cm` and whirled in a vertical circle. If a horizontal rightward electric field of strength `E = 10^5 NC^-1` exists in the space, calculate the minimum velocity of the sphere required at the highest point so that it may just complete the circle `(g = 10 ms^-2)`.

Explanation

To solve the problem, we need to find the minimum velocity of a sphere at the highest point of a vertical circle so that it can complete the circle under the influence of gravity and an electric field.

### Step-by-Step Solution:

1. **Identify the Known Values:**
- Mass of the sphere, \( m = 0.6 \, \text{kg} \)
- Charge of the sphere, \( q = 80 \, \mu\text{C} = 80 \times 10^{-6} \, \text{C} \)
- Length of the string (radius of the circle), \( r = 30 \, \text{cm} = 0.3 \, \text{m} \)
...