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Two tiny spheres of mass m = 8.80 m g carry charges of equal magnitude, 72.0 n C

ID: 2277375 • Letter: T

Question

Two tiny spheres of mass m = 8.80mg 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

What is the magnitude E of the field?

Two tiny spheres of mass m = 8.80mg 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

Explanation / Answer

r = 2 L sin(50) = 2*0.530 * sin(50) = 0.81201 m


x direction:

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

y direction:

T cos(theta) = m g


dividing them:

(T sin(theta))/(T cos(theta)) = (E q - k q^2/r^2)/(m g)

==> tan(theta) = (E q - k q^2/r^2)/(m g)

==> tan(50) = (E * 72e-9 - 9e9*72e-9/(0.81201*0.81201))/(8.8e-3*9.8)

==> 1.19175 = (E * 72e-9 - 9e9*72e-9/(0.81201*0.81201))/(8.8e-3*9.8)

==> 1.19175*(8.8e-3*9.8) = (E * 72e-9 - 9e9*72e-9/(0.81201*0.81201))

==> 0.10277652 = (E * 72e-9 - 9e9*72e-9/(0.81201*0.81201))

==> 982.874 = E * 72e-9

==> E = 1.37 x 10^10 N/C