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. Assuming the potential at the origin is zero, determine the expression for the potential at an arbitrary point (x, y, z) .
Options
- A-(2.0 V m ⁻¹) x
- B(2.0 V m ⁻¹) z
- C-(2.0 V m ⁻¹) y
- D(2.0 V m ⁻¹) x
Correct answer
A. -(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 from the origin (0,0,0) to an arbitrary point (x,y,z) : ₀^ V dV = - ₀^ x 2.0 dx V - 0 = -2.0 x Since 1 N C ⁻¹ = 1 V m ⁻¹ , the expression for the potential at (x,y,z) is -(2.0 V m ⁻¹) x