Two tiny spheres of mass 5.80 mg carry charges of equal magnitude, 77.0 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 θ between the strings equal to 58.0∘ what is the magnitude e of the field?

Mass m = 5.80 mg = 5.80 x 10⁻⁶ kg

Charge q = 77 nC = 77 x 10⁻⁹ C

String length L = 0.530 m

angle θ = 58.0°

Here we can force on one mass

gravitational force F1= mg is acting in downward direction

F1 = (5.80 x 10⁻⁶ kg)(9.81 m/s²)

F1 = 57 x 10⁻⁶ N

Second force is electrostatic force due to another charge

F2 = kqq/r₂

Where r is the distance between two charges

r = 2 LSinθ = 2(0.53)Sin58

r = 0.9 m

F2 = (9x 10⁹)(77 x 10⁻⁹)(77 x 10⁻⁹)/(0.9²)

F2 = 65.9 x 10⁻⁶ N

Third force is F3 = qE

Fourth force is tension in the string

In equilibrium sum of forces along horizontal will be zero

and sum of forces along vertical will be zero

First we will use sum of vertical forces equal to zero

TCosθ - F1 =0

T Cos58 - ( 57 x 10⁻⁶) = 0

T = 107.56 x 10⁻⁶ N

Now Sum of horizontal forces = 0

F3 - F2 - TSinθ = 0

qE - (65.9 x 10⁻⁶ ) - (107.56 x 10⁻⁶) = 0

(77 x 10⁻⁹) E = 173.46 x 10⁻⁶

E = 2253 N/C

positive reinforcement? ?

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force