Electric field in a region is given by E⃗=Axî+Byĵ, where A=10 V/m² and B=5 V/m². If the electric potential at a point (10,20) is 500 V , then the electric potential at origin is ____ V.

Solution

Physics sir · 3 steps

Integrate the field from the origin to (10, 20). Potential rises as you move against the field.

1. Link V and E. Potential falls along the direction of the field: dV = -E⃗· dr⃗ = -(Ax dx + By dy). Integrate from the origin O to the point P(10, 20).

   V_P - V_O = -[(A x²)/2 + (B y²)/2]_((0,0))^((10,20))

2. Put in numbers. (A x²)/2 = (10 × 100)/2 = 500 and (B y²)/2 = (5 × 400)/2 = 1000. So V_P - V_O = -(500 + 1000) = -1500 V.
3. So. V_O = V_P + 1500 = 500 + 1500 = 2000 V, which is option (c).

The idea to keep. Use V_B - V_A = -∫_A^B E⃗· dr⃗, and the x and y parts integrate separately. A point further along the field is always at lower potential.

Answer from the NTA final answer key. Solution by PrepWiser.