In the figure, a small spherical insulator of mass 6 In the figure, a small sphe

Question

In the figure, a small spherical insulator of mass 6

In the figure, a small spherical insulator of mass 6 times 10-2 kg and charge +0.4 ?C is hung by a thin wire of negligible mass. A charge of -0.22 ?C is held 0.29 m away from the sphere and directly to the right of it, so the wire makes an angle theta with the vertical, as shown. Draw the free-body diagram for the spherical insulator, indicating all the forces (electrical force, tension in the wire, and gravity). What is the angle theta for which the spherical ball is in equilibrium? (k = 9 times 109 N m2/C2).

Explanation / Answer

let tension be T.

the horizontal component of T balances the elctrical force and vertical component balances the weight

T*cos(theta)=6*0.01*9.8=0.588 N

T*sin(theta)=9*10^9*0.4*10^(-6)*0.22*10^(-6)/0.29^2=0.0094 N

squaring and adding,

T=0.588075 N

theta=0.9175 degrees

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