Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Field and Potential
A uniform field of 2.0 N C ⁻¹ exists in space in the x -direction. If the potential at the origin is set to 100 V , determine the expression for the potential at an arbitrary point (x, y, z) .
Options
- A100 V - (2.0 V m ⁻¹) y
- B100 V + (2.0 V m ⁻¹) x
- C(2.0 V m ⁻¹) x - 100 V
- D100 V - (2.0 V m ⁻¹) x
Correct answer
D. 100 V - (2.0 V m ⁻¹) x
Step-by-step solution
The relation between electric potential and electric field is given by dV = - E d r Given E = 2.0 i N C ⁻¹ and d r = dx i + dy j + dz k dV = -(2.0 i ) (dx i + dy j + dz k ) = -2.0 dx Integrating both sides from the origin (0,0,0) to an arbitrary point (x,y,z) : ₁₀₀^ V dV = ₀^ x -2.0 dx V - 100 = -2.0 x V = 100 - 2.0 x Since 1 N C ⁻¹ = 1 V m ⁻¹ , the expression for the potential is 100 V - (2.0 V m ⁻¹) x