Question

Two point charges −Q and Q are located at points (d, 0) and (0, d) respectively, in x-y plane. The electric field E at the origin will be ______.

Options

• `1/(4 pi epsilon_0) (sqrt2 Q)/d^2 (hat i - hat j)`

• `1/(4 pi epsilon_0) (sqrt2 Q)/d^2 (-hat i - hat j)`

• `1/(4 pi epsilon_0) Q/d^2 (hat i - hat j)`

• `1/(4 pi epsilon_0) Q/d^2 (-hat i - hat j)`

Answer 1

Two point charges −Q and Q are located at points (d, 0) and (0, d) respectively, in x-y plane. The electric field E at the origin will be `bbunderline(1/(4 pi epsilon_0) Q/d^2 (hat i - hat j))`.

Explanation:

Charge −Q is located at (d, 0). The distance from the origin is d. Since the charge is negative, the electric field `vec E_1` at the origin points toward the charge, i.e., along `+hat i`:

`vec E_1 = 1/(4 pi epsilon_0) Q/d^2 hat i`

Charge +Q is located at (0, d). The distance is d. Since it is positive, the electric field `vec E_2` at the origin points away from the charge, i.e., along `-hat j`:

`vec E_2 = 1/(4 pi epsilon_0) Q/d^2 (-hat j)`

The resultant electric field is the vector sum:

`vec E = vec E_1 + vec E_2`

= `1/(4 pi epsilon_0) Q/d^2 hat i - 1/(4 pi epsilon_0) Q/d^2 hat j`

= `1/(4 pi epsilon_0) Q/d^2 (hat i - hat j)`