Two point charges $Q_{1} = 400 μ C$ and $Q_{2} = 100 μ C$ are kept fixed, 60 cm apart in vacuum. Find intensity of the electric field at midpoint of the line joining $Q_{1}$ and $Q_{2}$ .

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Solution

$Step 1: Electric field at midpoint O due to both charges$
As, Distance between two charges, $d = 60 c m$ and O is the mid point.
So, $A O = B O = \frac{d}{2} = 30 c m$

At point O, electric field due to point charge kept at A,
$E_{1} = \frac{1}{4 π ϵ_{0}} \times \frac{Q_{1}}{r^{2}}$ $= 9 \times 10^{9} \times \frac{400 \times 10^{- 6}}{(30 \times 10^{- 2})^{2}}$ [in the direction of AO]

At point O, electric field due to point charge kept at B,
$E_{2} = \frac{1}{4 π ϵ_{0}} \frac{Q_{2}}{r^{2}}$ $= 9 \times 10^{9} \times \frac{100 \times 10^{- 6}}{(30 \times 10^{- 2})^{2}}$ [in the direction of BO]
$Step 2: Resultant Electric field at midpoint O$
So, resultant electric field $\to E =_{1} +_{2}$

$\to E = \frac{9 \times 10^{9}}{(30 \times 10^{- 2})^{2}} \times 10^{- 6} \times (400 - 100)$

$= \frac{9 \times 10^{9} \times 10^{- 6} \times 300}{900 \times 10^{- 4}}$

$= 3 \times 10^{7} N / C$ [in the direction of AO]

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Two point charges Q1=400μC and Q2=100μC are kept fixed, 60 cm apart in vacuum. Find intensity of the electric field at midpoint of the line joining Q1 and Q2.

Two point charges $Q_{1} = 400 μ C$ and $Q_{2} = 100 μ C$ are kept fixed, 60 cm apart in vacuum. Find intensity of the electric field at midpoint of the line joining $Q_{1}$ and $Q_{2}$ .