Two rings of radius 5 cm are 15 cm apart and concentric with a common horizontal -axis. The ring on the left carries a uniformly distributed charge of 33 nC, and the ring on the right carries a uniformly distributed charge of -33 nC. What is the magnitude and direction of the electric field on the -axis, halfway between the two rings

Explanation:

Radius of ring r = .05 m

Electric field due to a uniformly charged ring

E = k Q x  / ( x² + r² )³/²   ;  Q is charge on the ring , x is distance of point  from the center of the ring and r is radius of the ring

electric field due to first ring at middle point or at x = 7.5 cm

E = 9 x 10⁹ x 33 x 10⁻⁹ x 7.5 x 10⁻² / ( 7.5² + 5² )³/² x 10⁻³

= 9 x 10⁹ x 33 x 10⁻⁹ x 7.5  / ( 7.5² + 5² )³/² x 10⁻¹

= 9 x 10⁹ x 33 x 10⁻⁹ x 7.5 / 73.23

=  30.41 N/C

The same field will be created by the other ring at the middle point because charge on the ring is same in magnitude . Due to negative charge on the second ring , field due to both the rings will align in the same direction.

Total field = 2 x 30.41

= 60.82 N/C