ElectrostaticsHard

Question

Three charges, each +q, are placed at the corners of an isoscales triangle ABC of sides BC and AC, 2a. D and E are the mid point of BC and CA. The work done in taking a charge Q from D to E is
                 

Options

A.
B.
C.
D.zero

Solution

                       
Here AC = BC = 2a
D and E are the midpoints of BC and AC
∴ AE = EC = a and BD = DC = a
In ᐃADC, (AD)2 = (AC)2 - (DC)2
= (2a)2 - (a)2 = 4a2 - a2 = 3a2
AD = a√3
Similarly, BE = a√3
Potential at point D due to the given charge configuration is

.......(i)
Potential at point E due to the given charge configuration is

.......(ii)
From the (i) and (ii), it is clear that
VD = VE
The work done in taking a charge Q from D to E is
W = Q (VE - VD) = 0(∵ VD = VE)

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