Electric field vector in a region is given by E =(3 hat i +4 y hat j ) V - m -1. The potential at the origin is zero. Then, the potential at a point (2,1) m is

Question

Electric field vector in a region is given by E =(3 hat i +4 y hat j ) V - m -1. The potential at the origin is zero. Then, the potential at a point (2,1) m is (A) 7 V (B) 8 V (C) -8 V (D) -7 V

Tardigrade Admin · Accepted Answer

As, E=(- partial Vx/ partial x) hat i +(- partial Vy/ partial y) hat j (- partial Vx/ partial x) =3 and (- partial Vy/ partial y)=4 y ⇒ Vx =-3 x and Vy=-2 y2 So, V= potential function =(3 x+2 y2) Potential at point (2,1) is V=-(3 × 2+2 × 12)=-8 V

Q. Electric field vector in a region is given by E=(3i^+4yj^​)V−m−1. The potential at the origin is zero. Then, the potential at a point (2,1)m is

7 V

8 V

-8 V

-7 V

As, E=∂x−∂Vx​​i^+∂y−∂Vy​​j^​ ∂x−∂Vx​​=3 and ∂y−∂Vy​​=4y ⇒Vx​=−3x and Vy​=−2y2 So, V= potential function =(3x+2y2) Potential at point (2,1) is V=−(3×2+2×12)=−8V

Q. Electric field vector in a region is given by $E = (3 \hat{i} + 4 y \hat{j}) V - m^{- 1}$ . The potential at the origin is zero. Then, the potential at a point $(2, 1) m$ is