Question

4. Two identical charges are 25cm apart. They repel each other with the force of 2 x 10-6 Find Each

charge?

Answer 1

Both charges are of the same sign (positive or negative) and with a value of 3.73 ηc.

Step-by-step explanation:

Coulomb's Law

The electrical force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between the two objects.

Written as a formula:

`\displaystyle F=k(q_1q_2)/(d^2)`

Where:

`k=9\cdot 10^9\ N.m^2/c^2`

q1, q2 = the objects' charge

d= The distance between the objects

We know both charges are identical, i.e. q1=q2=q. Since the force is repulsive, both charges are positive or negative.

We also are given the force between them:

`F=2\cdot 10^(-6)\ N`

And also the distance

d=25 cm = 0.25 m

Substituting all into the formula:

`\displaystyle 2\cdot 10^(-6)=9\cdot 10^9(q.q)/(0.25^2)`

The product of
`q.q=q^2`. Operating:

`\displaystyle 2\cdot 10^(-6)=9\cdot 10^9(q^2)/(0.0625)`

Operating:

`\displaystyle 0.0625\cdot 2\cdot 10^(-6)=9\cdot 10^9\cdot q^2`

Solving for q:

`\displaystyle q^2=(0.0625\cdot 2\cdot 10^(-6))/(9\cdot 10^9)`

`q^2=1.39\cdot 10^(-17)`

`q=\sqrt{1.39\cdot 10^(-17)}=3.73\cdot 10^(-9)\ c= 3.73\ \eta c`

Both charges are of the same sign (positive or negative) and with a value of 3.73 ηc.