Question

three charged particles lie on an x axis. particle 1 and 2 are fixed in place. particle 3 is free to move, but the net electrostatic force on it from larticles 1 and 2 happens to be zero. if L23=4.45L12 what is the q1/q2 ratio? please answer w 5 decimal points

Answer 1

The
`\( (q_1)/(q_2) \)` ratio is 4.45000.

The ratio of the charges
`\( q_1 \) to \( q_2 \)` can be determined using Coulomb's Law, considering that the net electrostatic force on particle 3 is zero:

`\[ F_(23) = F_(13) + F_(23) = 0 \]`

Since
`\( F = k (q_1q_3)/(r_(13)^2) + k (q_2q_3)/(r_(23)^2) \) and \( L_(23) = 4.45L_(12) \)`, we can set up the ratio equation:

`\[ (q_1)/(q_2) = \left((r_(13))/(r_(23))\right)^2 * (L_(23))/(L_(12)) = \left((r_(13))/(r_(23))\right)^2 * (4.45)/(1) \]`

Given that the net electrostatic force on particle 3 from particles 1 and 2 is zero, the ratio of distances
`\( (r_(13))/(r_(23)) \)` is equal to 1.

Thus,
`\( (q_1)/(q_2) = 1^2 * 4.45 = 4.45 \).`