Three point charges Q1, Q2 and Q3 in that order are placed equally spaced along a straight line. Q2 and Q3 are equal in magnitude but opposite in sign. If the net force on Q3 is zero, the value of Q1 is

Given q2=q3 and let ;q2=+ve and q3=−veNet force on Q3=14πε0Q1Q34d2−14πε0Q3Q2d2Q1Q34d2=Q3Q2d2⇒Q1=4Q2

Three point charges Q1, Q2 and Q3 in that order are placed equally spaced along a straight line. Q2 and Q3 are equal in magnitude but opposite in sign. If the net force on Q3 is zero, the value of Q1 is

Given q2=q3 and let ;q2=+ve and q3=−veNet force on Q3=14πε0Q1Q34d2−14πε0Q3Q2d2Q1Q34d2=Q3Q2d2⇒Q1=4Q2

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Three point charges Q₁, Q₂ and Q₃ in that order are placed equally spaced along a straight line. Q₂ and Q₃ are equal in magnitude but opposite in sign. If the net force on Q₃ is zero, the value of Q₁ is

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$Q_{1} = | 4 | Q_{2} ∣$

$Q_{1} = \sqrt{2} |Q_{3}|$

$Q_{1} = |Q_{3}|$

$Q_{1} = 2 |A_{3}|$

answer is D.

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Detailed Solution

Given $|q_{2}| = |q_{3}| and let; q_{2} = + ve and q_{3} = - ve$
Net force on $Q_{3} = \frac{1}{4 π ε_{0}} \frac{Q_{1} Q_{3}}{4 d^{2}} - \frac{1}{4 π ε_{0}} \frac{Q_{3} Q_{2}}{d^{2}}$
$\frac{Q_{1} Q_{3}}{4 d^{2}} = \frac{Q_{3} Q_{2}}{d^{2}} \Rightarrow Q_{1} = 4 Q_{2}$