Question

Two 10-cm-diameter charged rings face each other, 15cm apart. The left ring is charged to -29nC and the right ring is charged to +29nC .

What is the magnitude of the electric field E?  at the midpoint between the two rings?

What is the magnitude of the force F?  on a -1.0 nC charge placed at the midpoint?

Answer 1

We will calculate electric field at mid point ie at point P from fig.

here r= distance of point P from charged ring

E1 = electric field at point P due to q1

E1 = k q1*r / ( r²+a²)^3/2                                    toward -ve charge

   = 9*10⁹*29*10^-9*7.5*10^-2 / [ ( 7.5*10^-2)² + ( 5*10^-2)² ] ^3/2

   = 26.74 *10³ N/C                         

E2 = electric field at point P due to q2 = k * q2*r / (r²+a²)^3/2

                             by putting values,   E2 = 26.74*10³ N/c

net electric field at point P , E = E1 +E2                        ( because E1 & E2 are in same direction)

E = 2E1                                 ( E1=E2)

= 53.48*10³ N/c                           ( direction is towards -Ve charge)

(b) force at midpoint,    F = q*E

F = - 1*10^-9*53.48*10³

= - 5.34*10^-5 N

-ve sign shows that its directionis opposite to E ie towards +ve charge.