A charge of -3.35 nC and a charge of -7.00 nC are separated by a distance of 40.0 cm. Find the position at which a third charge of +7.10 nC can be placed so that the net electrostatic force on it is zero.
well, it is fairly obvious a positive charge between two negatives can be placed at a zero force.
Let x be where the 3.35nC charge is.
Then ...
k3.35*7.10/x^2=k&*7/(.4-x)^2
solve for x.
To find the position at which the net electrostatic force on the third charge is zero, we can use Coulomb's Law. Coulomb's Law states that the force of attraction or repulsion between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
where:
F is the electrostatic force
k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
q1 and q2 are the charges
r is the distance between the charges
For a net force of zero, the magnitudes of the forces due to each pair of charges must be equal. So, we can set up an equation:
k * (q1 * q3) / r1^2 = k * (q2 * q3) / r2^2
where:
q1 = -3.35 nC = -3.35 x 10^-9 C
q2 = -7.00 nC = -7.00 x 10^-9 C
q3 = +7.10 nC = 7.10 x 10^-9 C
r1 = distance between charge q1 and q3 (unknown)
r2 = distance between charge q2 and q3 (unknown)
Now we can rearrange the equation to solve for r1:
(q1 * q3) / r1^2 = (q2 * q3) / r2^2
(q1 * q3 * r2^2) = (q2 * q3 * r1^2)
r1^2 = (q1 * r2^2) / q2
r1 = sqrt[(q1 * r2^2) / q2]
Substituting the given values:
q1 = -3.35 x 10^-9 C
q2 = -7.00 x 10^-9 C
q3 = 7.10 x 10^-9 C
r2 = 40.0 cm = 0.40 m
Plugging these values into the equation and solving:
r1 = sqrt[((-3.35 x 10^-9) * (0.40)^2) / (-7.00 x 10^-9)]
r1 = sqrt[(-5.36 x 10^-10) / (-7.00 x 10^-9)]
r1 = sqrt[0.07657]
r1 ≈ 0.277 m
Therefore, the position at which the third charge of +7.10 nC can be placed so that the net electrostatic force on it is zero is approximately 0.277 meters away from the charge of -3.35 nC.