Three identical point charges, each of mass m = 0.450 kg, hang from three string

Question

Three identical point charges, each of mass m = 0.450 kg, hang from three strings, In the figure below. If the lengths of the left and right strings are each L = 8.0 cm, an angle theta is 45 degree, determine the value of q. C A uniformly charged ring of radius 10.0 cm has a total charge of 86.0 mu C. Find the electric field on the axis of the ring at the following distances from the center of the ring. (Choose the x-axis to point along the axis of the ring.) (a) 1.00 cm i MN/C (b) 5.00 cm i MN/C (C) 30.0 cm i MN/C (d) 100 cm i MN/C

Explanation / Answer

here,

m = 0.45 kg

L = 0.28 m

theta = 45 degree

the distance bewteen the charges , d = L * sin(theta)

d = 0.198 m

for the left charge and the middle charge

let the tension in the left string be t

equating the forces vertically

t * sin(theta) = m * g ...(1)

and

equating the forces horizontally

t * cos(theta) = k * q * q/d^2 ...(2)

from (1) and (2)

tan(theta) = m * g * d^2 /( k * q^2)

tan(45) = 0.45 * 9.8 * 0.198^2 /( 9 * 10^9 * q^2)

solving for q

q = 4.38 * 10^-6 C

the magnitude of charge q is
4.38 * 10^-6 C

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