Asmall spherical insulator of mass 6.68 x 10^-2 kg and charge +0.600 c is hung by a thin wire of negligible mass. a charge of -0.900 c is held 0.150 m away from the sphere and directly to the right of it, so the wire makes an angle with the vertical (see the drawing). find (a) the angle and (b) the tension in the wire.

(a):

(b):

Explanation:

Given:

There are two forces that act on the sphere,

According to Coulomb's law, the magnitude of the electrostatic force between the charges is given as:

where, k is the Coulomb's constant whose value =

The weight of the sphere is given as:

is the acceleration due to gravity whose value =

(a):

According to the figure. the angle which the wire is making with the vertical is given as:

(b):

Both the forces, and are perpendicular to each other, therefore, the tension in the wire is given as:

step-by-step explanation:

we are given

we have to simplify it

firstly, we will factor it

now, we can cancel like terms

now, we can combine it

so, we get

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