Q.

Ten charges are placed on the circumference of a circle of radius R with constant angular separation 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 the circle are respectively.  (Take V = 0 at infinity)

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a

V=10q4π∈0R;E=0

b

V=0;E=0

c

V=10q4π∈0R;E=10q4π∈0R2

d

V=0;E=10q4π∈0R2

answer is B.

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Detailed Solution

Potential at point C  Potential is scalar quantity. Vc=5kqr+5k−qr=0Electric field at C Field is vector quantity. E→C=E→ due to+qs+E→ due to−qs= 0+0     from symmetry
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Ten charges are placed on the circumference of a circle of radius R with constant angular separation 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 the circle are respectively.  (Take V = 0 at infinity)