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  • Three charges, each +q, are placed at the corners of an isosceles triangle ABC of sides BC and AC, 2a. D and E are the mid points of BC and CA. T

Three charges, each +q, are placed at the corners of an isosceles triangle ABC of sides BC and AC, 2a. D and E are the mid points of BC and CA.

The work done in taking a charge Q from D to E is

Option: 1

Zero


Option: 2

\frac{3\text{qQ}}{4\pi\varepsilon_{0}\text{a}}


Option: 3

\frac{3\text{qQ}}{8\pi\varepsilon_{0}\text{a}}


Option: 4

\frac{\text{qQ}}{4\pi\varepsilon_{0}\text{a}}


Answers (1)

best_answer

 

Given:
AC=BC and D & E are midpoints of BC and AC respectively.
?DC=DB=EC=EA

Also, using geometry it can be proved that BE=DA

As all charges at A, B and C are equal and distances of D and E from A, B and C are also equal, it can be concluded from symmetry that the potentials at D and E are equal. 

The work done in taking a charge Q from D to E is independent of the path taken and is given by

\begin{array}{l} V_{D}=V_{E}=V \\ W=Q\left[V_{E}-V_{D}\right] \\ W=Q[V-V] \\ W=0 \end{array}

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shivangi.shekhar

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