Two point charges -Q and +Q / 3 are placed in the x y -plane at the origin (0,0) and a point (2,0) , respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V=0 in the x y -plane with its center at (b, 0) . All lengths are measured in meters. The value of R is ________ meter.

Step-by-step solution

Let P h , k be be a general point with potential to be zero. V 1 + V 2 = 0 (as potential given = 0 ) K − Q h 2 + k 2 + K Q 3 h − 2 2 + k 2 = 0 1 3 h − 2 2 + k 2 = 1 h 2 + k 2 3 h − 2 2 + k 2 = h 2 + k 2 3 h 2 − 4 h + 4 + k 2 = h 2 + k 2 2 h 2 + 2 k 2 − 12 h + 12 = 0 h 2 + k 2 − 6 h + 6 = 0 h 2 − 6 h + 6 + k 2 = 0 h 2 − 6 h + 9 + k 2 = 3 h − 3 2 + k 2 = 3 Standard equation of circle is given by x − x 1 2 + y − y 1 2 = R 2 ∴     x