Two tiny spheres of mass m = 7.60 m g carry charges of equal magnitude, 72.0 n C

Question

Two tiny spheres of mass m = 7.60mg carry charges of equal magnitude, 72.0 nC, but opposite sign. They are tied to the same ceiling hook by light strings of length 0.530 m. When a horizontal uniform electric field E that is directed to the left is turned on, the spheres hang at rest with the angle ? between the strings equal to 50.0?in the following figure. (Figure 1)

What is the magnitude E of the field? Please include units!!

A rightarrow B rightarrow C rightarrow A rightarrow B rightarrow C rightarrow A rightarrow B rightarrow C rightarrow B rightarrow C rightarrow

Explanation / Answer

let r is the distance between the charges

sin(25) = (r/2)/L

r = 2*L*sin(25) = 0.45 m

at equilibrium,

in y-direction, T*cos(25) = m*g

T = m*g/cos(25) = 0.0822 N

in x-direction, q*E + T*sin(25) = k*q^2/r^2

E = k*q^2/r^2 - T*sin(25)

E = 2.3*10^-4 - 347.3*10^-4

E = 345*10^-4 = -3.45 m N/C

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