A uniform electric field of `100 Vm^-1` is directed at `30^(@)` with the positive x - axis as shown in (Fig. 3.153). `O A = 2 m` and `O B = 4 m`.
.
The potential difference `V_O - V_A` is.

Options

A. `100 sqrt(3) V`
B. `200 sqrt(3) V`
C. `-100 sqrt(3) V`
D. `-200 sqrt(3) V`

Answer

C

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`.