Question

Two small conducting point charges, separated by 0.6 m, carry a total charge of 185 mu or micro CC. They repel one another with a force of 120 N. For the universal constant k use the value 8.99 times 109 N m2/C2. Find the charge on the larger of the two point charges:

Answer 1

Step-by-step explanation:

Let the two charges are q and Q.

According to the question

q + Q = 185 micro Coulomb .... (1)

Force of repulsion, F = 120 N

distance, d = 0.6 m

K = 8.99 x 10^9 Nm²/C²

Use Coulomb's law

`F = (kQq)/(d^(2))`

`120= (8.99* 10^(9)Q\left ( 185-Q \right )* 10^(-12))/(0.6^(2))` .... from equation (1)

4805.4 = 185 Q - Q²

Q² - 185 Q + 4805.4 = 0

`Q=\frac{185\pm \sqrt{185^(2)-4* 4805.4}}{2}`

Q = 153.75 μC, 31.25 μC

q = 185 - 153.75 = 31.25 μC, 185 - 31.25 = 153.75 μC

So, charges are

31.25 μC, 153.75 μC