Question

two point charges Q and -3Q are placed at some distance apart .if the electric field at the location of Q is E bar the field at the location of -3Q is
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Answer 1

electric field at the location of -3Q is $\frac{\vec E}{3}$.

It has given that two charge Q and -3Q are placed at some distance apart. the electric field at the location of Q is $\vec E$.

we have to find electric field at the location of -3Q.

let Q and -3Q are placed r distance apart.

Q --------------------(r)----------------- -3Q

electric field due to -3Q at the location of Q = k(3Q)/r² = 3kQ/r²

⇒$\vec E$ = 3kQ/r² towards -3Q (i.e., along east direction).......(1)

now electric field due to Q at the location of -3Q , E₁ = k(Q)/r² towards -3Q (i.e., along east direction)

from equation (1) we get,

E₁ = $\frac{\vec E}{3}$

Therefore electric field at the location of -3Q is $\frac{\vec E}{3}$.