Question

Two electric charges q1 and 5q1 are 3cm apart and apply a repulsive force of 0.02N to each other. How many microculons is q1?

Sorry if it's a bit vague, I had to use a translator​

Answer 1

q(1) = q

`\frac{k.q.5q}{ ({3 * {10}^( - 2) })^(2) } = 2 * {10}^( - 2) \\`

`\frac{9 * {10}^(9) * 5 {q}^(2) }{9 * {10}^( - 4) } = 2 * {10}^( - 2) \\`

9s simplify

`\frac{ {10}^(9) * 5 {q}^(2) }{ {10}^( - 4) } = 2 * {10}^( - 2) \\`

Multiply sides by 10^-4

`5 {q}^(2) * {10}^(9) = 2 * {10}^( - 2) * {10}^( - 4)`

`5 {q}^(2) * {10}^(9) = 2 * {10}^( - 6)`

Divided sides by 10⁹

`5 {q}^(2) = \frac{2 * {10}^( - 6) }{ {10}^(9) } \\`

`5 {q}^(2) = 2 * {10}^( - 6) * {10}^( - 9)`

`5 {q}^(2) = 2 * {10}^( - 15)`

Divided sides 5

`{q}^(2) = (2)/(5) * {10}^( - 15) \\`

`{q}^(2) = (4)/(10) * {10}^( - 15) \\`

`{q}^(2) = 4 * {10}^( - 1) * {10}^( - 15)`

`{q}^(2) = 4 * {10}^( - 16)`

`q = \sqrt{4 * {10}^( - 16) }`

`q = 2 * {10}^( - 8)`

`q = 2 * {10}^( - 2) * {10}^( - 6)`

`q = 2 * {10}^( - 2) \: \: \: μc`