When a test charge is brought in from infinity along the perpendicular bisector of an electric dipole, the work done is zero. How ?

Because electric potential at the equatorial line is zero.
     work done = electric potential X charge 
                        = 0                                     (V=0)

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THE WORK DONE IS ZERO.
LETS SAY
THE POSITIVE POLE OF DIPOLE DOES A POSITIVE WORK. THEN THE WORK DONE BY NEGATIVE DIPOLE WILL BE SAME IN MAGNITUDE BUT NEGATIVE. IF POSITIVE POLE WILL REPEL TEST CHARGE THEN THE NEGATIVE WILL ATTRACT IT WITH SAME MAGNITUDE, THUS THE NET WORK BECOMES ZERO.
 
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Since Work Done = Electric potential * Charge and potential along the perpendicular axis in an electric dipole is zero , so work done is zero
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