Question

The electric field in a region is given by `vec"E"` = (Ax + B) `hat"i"`, where E is in NC^-1 and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V₁ and that at x = -5 is V₂, then V₁ - V₂ is ______.

Options

• 320 V

• -48 V

• 180 V

• -520 V

Answer 1

The electric field in a region is given by `vec"E"` = (Ax + B) `hat"i"`, where E is in NC^-1 and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V₁ and that at x = -5 is V₂, then V₁ - V₂ is 180 V.

Explanation:

Given, `vec"E" = ("A"x + "B")hat"i"` or E = 20x + 10

Using V = `-int "Ed"x`, we have

V₂ - V₁ = `int_-5^1`(20x + 10) dx = - 180 V

or V₁ - V₂ = 180 V