Question

Two point charges 1 µC and 4 µC are placed at x = 0 m and x = 3 m on x-axis respectively. The position between the two charges where net electric field is zero is

Answer 1

the answer will be '1m'

REFER TO THE ATTACHMENT FOR THE ANSWER

Answer 2

Answer:

Two-point charges 1 µC and 4 µC are placed at x = 0 m and x = 3 m on x-axis respectively. The position between the two charges where the net electric field is zero is 1m from the first charge

Explanation:

• The electric force due to two point charges ($q_{1} ,q_{2}$) separated by a distance (r) is given by the formula

       $E=K\frac{q_{1} q_{2} }{r^{2} }$

       where the constant $K=9*10^{9}$

From the question, we have two charges arranged as below

Let the third charge Q be placed at a distance (x) from the first charge

Force on it due to $q_{1}$ is $F_{1} =\frac{Kq_{1} Q}{x^{2} }$

Force on it due to $q_{2}$ is $F_{2} =\frac{Kq_{2} Q}{(3-x)^{2} }$

no net force on the third charge means, the charge is at equilibrium

that is the force on (Q) due to the two charges are equal and opposite

⇒ $\frac{Kq_{1} Q}{x^{2} }=\frac{Kq_{2} Q}{(3-x)^{2} }$

⇒$\frac{K*1*Q}{x^{2} } =\frac{K*4*Q }{(3-x)^{2} }$

⇒$\frac{1}{4} =\frac{x^{2} }{(3-x)^{2} }$

take square root

⇒$1/2=x/3-x$

cross multiply

⇒

$3-x=2x\\3=3x\\x=1$

the third charge should place at a distance $1m$ from the first charge