Three charges , and are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if is equal to [2000]

Question

Three charges $Q$ , $+ q$ and $+ q$ are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if $Q$ is equal to [2000]

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(2)

Since net electrostatic energy $+ q$

$∴$ $\frac{Q q}{a} + \frac{q^{2}}{a} + \frac{Q q}{a \sqrt{2}} = 0$

or $Q \sqrt{2} + q \sqrt{2} + Q = 0$

$∴$ $Q = - \frac{q \sqrt{2}}{\sqrt{2} + 1} = - \frac{2 q}{2 + \sqrt{2}}$

Solution

Q.
Three charges $Q$ , $+ q$ and $+ q$ are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if $Q$ is equal to [2000]

1 $\frac{- q}{1 + \sqrt{2}}$

2 $\frac{- 2 q}{2 + \sqrt{2}}$

3 $- 2 q$

4 $+ q$

Ans.
(2)

Since net electrostatic energy $Σ u = 0$

$∴$ $\frac{Q q}{a} + \frac{q^{2}}{a} + \frac{Q q}{a \sqrt{2}} = 0$

or $Q \sqrt{2} + q \sqrt{2} + Q = 0$

$∴$ $Q = - \frac{q \sqrt{2}}{\sqrt{2} + 1} = - \frac{2 q}{2 + \sqrt{2}}$

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Solution

Q. Three charges Q, +q and +q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to [2000]

1 -q1+2

2 -2q2+2

3 -2q

4 +q

Ans. (2) Since net electrostatic energy Σu=0 ∴ Qqa+q2a+Qqa2=0 or Q2+q2+Q=0 ∴ Q=-q22+1=-2q2+2