Question:

Two point charges $Q$ and $-3Q$ are placed certain distance apart. If the electric field at the location of $Q$ be $\overrightarrow{E}$, then that at the location of $-3Q$ will be :

Updated On: Jul 7, 2022
  • $3\,\overrightarrow{E}$
  • $-3\,\overrightarrow{E}$
  • $\overrightarrow{E}/3$
  • $-\overrightarrow{E}/3$
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The Correct Option is B

Solution and Explanation

Given, point charges: $Q$ and $-3 Q$ electric field at $Q=\vec{E}$ Let the electric field around $Q$ ? And electric fidd around $-3 Q=E_{2}$. $ E_{1}=\frac{R Q}{r^{2}}=\bar{E} \quad\left[r=\operatorname{small}_{\text {around }} Q_{\text {distance }}\right] \text {. } $ similarly, $ \begin{aligned} E_{2} &=\frac{k(-3 Q)}{r^{2}} \\ &=\frac{-3 k Q}{r^{2}}=(-3)\left[\frac{k Q}{r^{2}}\right] . \\ E_{2} &=-3 \vec{E} \end{aligned} $ Thus, the electric field at location of $-3 Q$ charge will be $-3 \vec{E}$.
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Notes on Electric Field

Concepts Used:

Electric Field

Electric Field is the electric force experienced by a unit charge. 

The electric force is calculated using the coulomb's law, whose formula is:

\(F=k\dfrac{|q_{1}q_{2}|}{r^{2}}\)

While substituting q2 as 1, electric field becomes:

 \(E=k\dfrac{|q_{1}|}{r^{2}}\)

SI unit of Electric Field is V/m (Volt per meter).