Question

Two 10-cm-diameter charged rings face each other, 23 cm apart. The left ring is charged to -24 nC and the right ring is charged to +24 nC .

Part A

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

Express your answer to two significant figures and include the appropriate units.

Part C

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

Express your answer to two significant figures and include the appropriate units.

Answer 1

Field at centre C due to each ring is = KQ(x/r³) = KQ(x/(sqrt(x²+R²))³)=

=9 x 10⁹ x 24 x 10^-9x(0.115/(sqrt(0.115^2+0.05^2)^3) = 12596.95 = 12597 N/C

a) As the field due to each ring act in the same direction the total field strength is twice due to each ring(=2*E) and direction towards -24 nC to the left
Total Field strength at the centre = 2 x 12597 = 25194 N/C <----

c)The magnitude of the force on a -1nC = q x Field strength at the mid point

-1 x 10 ^-9 x 25194 = 25.194 x 10^-6 N = 25.194 uN direction to the right