Question

) In the figure, two conducting balls of identical mass m = 10g and identical charge q hang from nonconducting threads of length L = 100cm. If x = 7.4cm, what is q? Since x is much smaller than L approximate sin(?) by ?

Answer 1

let the angle theta be x.so,

we just need to balance the electrostatic forces and the gravitational forces to get the results.

so,

the electrostatic force= kq1q2/r^2

=k*q^2/x^2

the gravitational force on the ball=mg

so, balancing the forces perpendicular to the string,

mgsin(x)=kq^2/x^2 * cos(x)

or mg*tan(x)=kq^2/x^2

also, since l>>x,

tan(x)=sin(x)~x/(2L)

so,

mgx/2L=kq^2/x^2

or 10*10^-3*9.81*7.4*10^-2/(2*1)=9*10^9*q^2/0.074^2

or q=4.7*10^-8 C

so the value of q is 4.7*10^-8 C

Answer 2

sin ? =

Answer 3

In the vertical direction, the Tension in the string is balanced by the mass

Tcos(angle) = mg

The angle (theta) is found from the sin function

sin(angle) = .0037/1

angle = 2.12 degrees

T(cos 2.12) = (.01)(9.8)

T = .0981

Then in the horizontal, Tsin(angle) = kqq/r^2

(.0981)(sin 2.12) = (9 X 10^9)(q^2)/(.074)^2

q = 4.70 X 10^-8 C

That is 47.0 nC