Question

point charges q1=50 uc and q2=-25 uc are placed 1 m apart. what is the force on a third chare q3=2 uc placed midway between q1 and q2? where must q3 of the preceding problem be placed so that the net force on it is zero?

Answer 1

d = -1 m

The negative sign indicates that the charge from that force of the space of the two spheres.

Step-by-step explanation:

That is a problem of electric forces, given by Coulomb's law

F =
`k ( q1q2)/(r^2)`

We use that charges of the same sign repel and charges of different signs do not attract, so the net force is

∑ = F₁₃ + F₂₃

F_ {net} =
`k (q_1q_3)/(r_(13)^2) + k (q_2q_3)/( r_(23)^)`

a) the charge is placed at the midpoint between the other two

r₁₃ = r₁₂ = R = ½ m = 0.5m

F_ {net} =
`(k)/(R^2 ) \ q3 ( q1+q2)`

calculate us

F_ {net} = 9 10⁹ / 0.5² 2 10⁻⁶ (50 -25) 10⁻⁶

F_ {net} = 1,800 N

b) where must be placed q3 so that the force is zero

for this case the charge q3 is outside the spheres

∑ F = 0

F₁₁₃ = F₂₃

k q_1 / r_{13}² = k q₂ q₃ / r₂₃²

q₁/ r₁₂² = q₂ / r₂₃²

suppose the distance

r₁₂ = d

the he other sphere is

r₂₃ = d + 1

we substitute

q₃ / d² = q₂ / (d + 1) ²

(d + 1) ² = q₂ / q₃ d²

d² (1 - q₂/ q₃) + 2d + 1 = 0

we solve the equation of a second

d = [-2 +
`√(2^2 - 4 1 ( 1+25/50)` ] / 2

d = -2 /2

d = -1 m

The negative sign indicates that the charge from that force of the space of the two spheres.