Question

Two 10-cm-diameter charged rings face each other, 25.0cm apart. Both rings are charged to +20.0nC. What is the electric field strength at:a) the midpoint between the two rings?b) the center of the left ring?

Answer 1

Answer:

1. Electric field strength mid point is 0 N/C.

2. Electric field strength at the center of the left ring is 5420 N/C

Explanation:

D of Ring = 10cm =0.1 Meter

Charge on each Ring = Q1=Q2=40*10-9 C

Radius = D/2 = .1/2= 0.05m.

E= 1/(4piε) * (xQ/(x2+r2)^3/2)

Distance from the left ring t the mid point is x = 0.25/2 =0.125

1/4piε=8.99x10^9

E=1.8x10^4 N/C

Emid=Eleft-Eright

as Eleft=Eright

Emid=0 N/C

for Ecenter of Ring

x=0.25m

E=5.42x10^3 N/C

Answer 2

The electric field strength at the midpoint of the rings is 0 N/C.

The electric field strength at the center  of the left ring is 2710.84 N/C.

The given parameters:

• Diameter of the rings, d = 10 cm
• Distance between the rings, r = 25 cm
• Charge of the rings, q = 20 nC

The electric field strength at the midpoint of the rings is calculated as follows;

$E_{net} = E_1 + E_2\\\\ E_{net} = E_1(+ve) - E_2(-ve) = 0$

The electric field strength at the center  of the left ring is calculated as follows;

$E = \frac{kqL}{(R^2 + L^2)^{3/2}} \\\\ E = \frac{9\times 10^9 \times 20\times 10^{-9} \times 0.25 \ }{(0.05^2 + 0.25^2 )^{3/2}} \\\\ E = 2710.84 \ N/C$

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