Question

Consider the following figure of two charged spheres suspended from insulating strings as shown 2. Suppose the charge q on each small sphere is 1.0 μC, the distance a is 30 cm, and L = 50 cm Determine the best match for each item.

Answer 1

Given is:-

Charge on each sphere is  

Given is: - Charge on each sphere is q = 1 times 10^-6 C a = 30 cm, L = 50 cm distance between the two spheres is d = 2a or d = 60 cm Now, Part-1 As the system is in equilibrium all the forces satisfy one another therefore The net force on each sphere is zero Part - 2 the electro static force between the two charged particles is given by F_e = K q_1 q_2/d^2 by plugging all the values we get F_e = (9 times 10^9) (1 times 10^-6) (1 times 10^-6)/(6 times 10^-2)^2 which gives us F_e = 0.025 N This is the electrostatic force which is experienced by each sphere Now, the free body diagram of all the forces is shown below: Therefore F_e = T sin theta by substituting all the values we get 0.025 = T (alpha./L) In the right angle triangle sine (angle) =

distance between the two spheres is d = 2a or

Now,

Part-1

As the system is in equilibrium all the forces satisfy one another therefore

The net force on each sphere is zero

Part - 2

the electro static force between the two charged particles is given by

by plugging all the values we get

which gives us

   This is the electrostatic force which is experienced by each sphere

Now,

the free body diagram of all the forces is shown below:

Therefore

by subsituting all the values we get

In the right angle triangle sine (angle) = perpendicular / hypotenuse

which gives us

this is the value of Tension in each string

Part-3

Again from the free body diagram the weight of the sphere is

by plugging all the values we get

which gives us

Part-4

ELectric force on right sphere is

Part-5

Electric force on the left sphere is

Part-6

Angle of string with the horizontal is

Part-7