Question

Two point charges are separated by a distance r and repel each other with forces of magnitude F. If their separation is reduced to 0.281 times the original value, what is the magnitude of the forces of repulsion

Answer 1

Answer: F2 = 0.00789f

Explanation: The force of attraction or repulsion between 2 charges is given by columb's.

The mathematical statement of this law explains that the force of attraction or repulsion (f) is inversely proportional to square of distance between the charges (r²).

F α 1/r², F = k/r²

Hence, k = F * r²

F1 * (r1)² = F2 * (r2) ²

From the question, F1 = f, r1 = r, F2 =?, r2 = 0.281r

By substituting all these parameters into the equation, we have that

f/r² = F2/ ( 0.281r)²

f/r² = F2/ 0.00789r²

By cross multiplying

f * 0.00789r² = F2 * r²

F2 = f * 0.00789r²/r²

F2 = 0.00789f.

The force of repulsion is 0.00789 times the initial force

Answer 2

12.66 times the original value.

Step-by-step explanation:

Using the Coulomb's law that states that "the force of attraction or repulsion exerted between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between these charges."

As stated in the law,

The force of repulsion (F) between two point charges is inversely proportional to the distance (r) between these two charges. This means that as the distance increases, the force will decrease and vice versa. i.e;

F ∝
`(1)/(r^(2) )`

=> F = k /
`r^(2)`

=> F
`r^(2)` = k

=>
`F_(1)r_(1) ^(2) = F_(2)r_(2) ^(2)` --------------------------(i)

Where;

`F_(1)` and
`F_(2)` are initial and final magnitudes of the force of repulsion/attraction

`r_(1)` and
`r_(2)` are the initial and final distances of separation.

According to the question,

r has been reduced to 0.281 of the original value. This means that;

`r_(2) = 0.281r_(1)`

Substituting
`r_(2) = 0.281r_(1)` into equation (i) gives;

=>
`F_(1)` x
`r_(1) ^(2)` =
`F_(2)` x (0.281
`r_(1)`)²

=>
`F_(1)` x
`r_(1) ^(2)` =
`F_(2)` x
`0.281^(2)` x
`r_(1) ^(2)`

Dividing both sides by
`r_(1) ^(2)` to eliminate it, we have;

=>
`F_(1)` =
`F_(2)` x
`0.281^(2)`

=>
`F_(1)` =
`F_(2)` x 0.07896

Making
`F_(2)` the subject of the formula

=>
`F_(2)` = 12.66 x
`F_(1)` -------------------- (ii)

From equation (ii),

It is evident that the magnitude of the forces of repulsion has increased to 12.66 times the original value.