A small sphere of mass `m = 0.5 kg` carrying a positive charge `q = 110 mu C` is connected with a light, flexible, and inextensible string of length of length `r = 60 cm` and whirled in a vertical circle. If a vertically upward 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 step by step, we will follow the reasoning laid out in the video transcript while ensuring clarity in each step:

### Step 1: Identify Given Values
We have the following values provided in the problem:
- Mass of the sphere, \( m = 0.5 \, \text{kg} \)
- Charge of the sphere, \( q = 110 \, \mu C = 110 \times 10^{-6} \, C \)
- Length of the string (radius of the circle), \( r = 60 \, \text{cm} = 0.6 \, \text{m} \)
- Electric field strength, \( E = 10^5 \, \text{N/C} \)
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