Question

The electric potential at a region in terms of the coordinates \((x,y,z)\) in metre is

\[ V(x,y,z)=\left(10-3x^2-y^2-1.5z^2\right)\times10^6\ \text{V}. \]
The magnitude of the electric force acting on a charge of \(2\,\mu\text{C}\) placed at the point \((1,1,3)\,\text{cm}\) is

• A. \(0.33\,\text{N}\)
• B. \(0.11\,\text{N}\)
• C. \(0.44\,\text{N}\)
• D. \(0.22\,\text{N}\)

Hint:

Electric field from potential: \[ \boxed{ \vec E=-\nabla V } \] and electric force is \[ \boxed{ \vec F=q\vec E. } \]

Answer 1

The Correct Option is D