Ten charges are placed on the circumference of a circle of radius R with constant angular sepration between successive charges. Alternate charges 1.3.5.7.9 have charge (+q) each while 2,4,6,8,10 have charge (-q) each. The potential V and the electric field E at the centre of circle are respectively (Take V =0 at w):
Option: 1 V=0, E=0 
Option: 2 V = \frac{10q}{4\pi E_{0}R}, E=\frac{10q}{4\pi E_{0}R^{2}}
Option: 3 V =0, E=\frac{10q}{4\pi E_{0}R^{2}}
Option: 4 V = \frac{10q}{4\pi E_{0}R}, E=0

Answers (1)

Correct Answer: a) V=0, E=0

As electric field is a vector quantity, so the electric due to each charge will cancel out each other due to symmetry as equal number of positive and negative charges are present at equal distances from the centre. And potential is a scalar quantity, it will also be zero as potential due to 5 positive charges will cancel the potential due to 5 negative charges

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