(D) The potential energy of a system of point charges is given by $U = \sum \frac{k q_i q_j}{r_{ij}}$.For the initial state with side $a_1 = 1 \ m$:$U

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(D) The potential energy of a system of point charges is given by $U = \sum \frac{k q_i q_j}{r_{ij}}$.For the initial state with side $a_1 = 1 \ m$:$U_i = \frac{1}{4 \pi \varepsilon_0} [\frac{(1)(-2)}{1} + \frac{(-2)(-2)}{1} + \frac{(-2)(1)}{1}] = \frac{1}{4 \pi \varepsilon_0} [-2 + 4 - 2] = 0 \ J$.For the final state with side $a_2 = 2 \ m$:$U_f = \frac{1}{4 \pi \varepsilon_0} [\frac{(1)(-2)}{2} + \frac{(-2)(-2)}{2} + \frac{(-2)(1)}{2}] = \frac{1}{4 \pi \varepsilon_0} [-1 + 2 - 1] = 0 \ J$.The work done by an external force is $W_{ext} = U_f - U_i = 0 - 0 = 0 \ J$.

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Three point charges $1 \ C$,$-2 \ C$,and $-2 \ C$ are placed at the vertices of an equilateral triangle of side $1 \ m$. The work done by an external force to increase the separation of the charges to $2 \ m$ in joules is $(\varepsilon_0 = \text{permittivity of air})$

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A
$\frac{1}{4 \pi \varepsilon_0}$
B
$\frac{1}{8 \pi \varepsilon_0}$
C
$\frac{1}{16 \pi \varepsilon_0}$
D
$0$

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Three point charges $1 \ C$,$-2 \ C$,and $-2 \ C$ are placed at the vertices of an equilateral triangle of side $1 \ m$. The work done by an external force to increase the separation of the charges to $2 \ m$ in joules is $(\varepsilon_0 = \text{permittivity of air})$

Similar Questions

Which one of the following is a correct set?

Cobalt $(III)$ chloride forms several octahedral complexes with ammonia. Which of the following will not give a test for chloride ions with silver nitrate at $25\,^{\circ}C$?

Two point white dots are $1 \, mm$ apart on black paper. They are viewed by an eye with a pupil diameter of $3 \, mm$. Approximately,what is the maximum distance at which these dots can be resolved by the eye? (Take $\lambda = 500 \, nm$)

$A$ tangent galvanometer has a coil of $25$ turns and a radius of $15 \, cm$. The horizontal component of the earth's magnetic field is $3 \times 10^{-5} \, T$. The current required to produce a deflection of $45^o$ in it is.....$A$

The cold junction of a thermocouple is at $0^{\circ} C$. The thermo e.m.f produced in the thermocouple is given by the equation $E = 16T - 0.04T^2$,where $T$ is the temperature of the hot junction. The temperature of inversion and neutral temperature of the thermocouple are:

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