COMEDK202510 May 2025Morning ShiftPhysicsElectrostaticsActual
An electric field E=3 x^2 i N C⁻¹ exists in a certain region of space. The potential difference between the origin and at x=4 m, V₀-V₄ is
Options
- A-20 ~V
- B64 V
- C-64 ~V
- D-40 ~V
Correct answer
B. 64 V
Step-by-step solution
The relationship between electric field E and electric potential V is given by dV = - E d r . Given E = 3x^2 i , we have dV = -3x^2 dx . To find the potential difference V₀ - V₄ , we integrate from x=4 to x=0 : V₀ - V₄ = ₄⁰ -3x^2 dx . V₀ - V₄ = -3 ₄⁰ x^2 dx . V₀ - V₄ = -3 [ x^3 3 ]₄⁰ . V₀ - V₄ = -[x^3]₄⁰ = -(0^3 - 4^3) = -(-64) = 64 V . Answer: 64 V