A uniform electric field of `100 V//m` is directed at `30^@` with the positive x-axis as shown in figure. Find the potential difference `V_(BA)` if `OA=2`m and `OB=4 m.`

Options

A. `-100 [2 + sqrt(3)] V`
B. `100 [2 + sqrt(3)] V`
C. `100[2 - sqrt(3)] V`
D. `-100[2 - sqrt(3)] V`

Answer

A

Explanation

`d_1 = AO cos 30^(@) = 2 sqrt(3)//2 = sqrt(3) m`
.
`d_2 = BO sin 30^(@) = 4 xx (1)/(2) = 2m`
`V_A - V_O = E d_1 = 100 sqrt(3) V`
`V_O - V_A = -100 sqrt(3) V`
`V_A - V_B = E (d_1 + d_2) = 100(sqrt(3) + 2) V`
`V_B - V_A = -100 (sqrt(3) + 2) V`.