Two tiny beads are 25 cm apart with no other charges or fields present. Bead A carries 10 µC of charge and bead B carries 1 µC. Which one of the following statements is true about the magnitudes of the electric forces on these beads?

Answer

1-The force on B is 10 times the force on A.

2-The force on B is 100 times the force on A.

3-The force on A is 100 times the force on B.

4-The force on A is 10 times the force on B.

5-The force on A is exactly equal to the force on B.

5-The force on A is exactly equal to the force on B.

Explanation:

This is proven mathematically:

The force on A by B is given as:

F (A, B) = [K * Q (A) * Q (B) ] / R²

The force on B by A is given as:

F (B, A) = [K * Q (B) * Q (A) ] / R²

Where K = Coulombs constant

R is the distance between them

Examining the two formulas closely show that they yield the same result.

5-The force on A is exactly equal to the force on B.

Explanation:

According to coulombs law of electrostatic attraction which states that the force of attraction that exists between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between the charges. Mathematically;

F = kq1q2/r² where q1 and q2 are the charges

r is the distance between them

k is the coulombs constant = 9*10^9Nm²/C²

Magnitude of the forces of one charge on the other will always be the same.

Given two beads A and B with charges 10µC and 1µC respectively separated by a distance of 25cm, the force exerted by A on B can be expressed as;

F (A, B) = kqAqB/r²

F (A, B) = (9*10^9 * 10*10^-6 * 1*10^-6) / 0.25²

F (A, B) = 1.44N

Similarly the force exerted by B on A is expressed as;

F (B, A) = kqBqA/r²

F (B, A) = 1.44N (no matter the arrangement of the charge)

This shows that the force exerted by A on B is equal to the force exerted by B on A, hence it can be concluded that the force on A is exactly equal to the force on B.