Question

A charged particle Q is at position $(2,-1,3)$. The electrostatic force on another charged $q_2$ at origin is :

• A. $14N$
• B. $13N$
• C. $15N$
• D. $16N$

Answer 1

Answer: (A)

$14N$

Given, charged particle $q_1$ Position $(2,-1,3)$ and $q_2$ position $(0,0,0)$

Let position vector of $q_1=OP=2i-j+3k$

Position vector of $q_2=OQ=0i+0j+0k$

Now, vector $PQ$,(separation between changes)=$OP-OQ=2i-j+3k$

Magnitude of $PQ={\sqrt{2}}^2+1^2+3^2=\sqrt{1}4$units

Now, electrostatic force in vector form.

$F=\frac{K{Q}_1{Q}_2}{{\left[r\right]}^3}r$

here $r$ is the separation between charges.

$F=\frac{K{q}_1{q}_2}{{\sqrt{14}}^3}\left(2i-j+3k\right)$

Magnitude of force $\frac{K{q}_1{q}_2}{{\sqrt{14}}^3}=14N$

Hence, Option $A$ is correct.