Two spheres with charges of 4.00nC and 3.00nC are placed 0.500m apart. At what point between the two charges must the third charge of 2.00cN be placed so that the net electrostatic force acting on this charge is zero?
k •q1 •q3/x^2 = k •q2 •q3/(d-x)^2
q1 •q3 (d-x)^2 = k •q2 •q3• x^2
Solve for x
The second line
q1 •q3 (d-x)^2 = q2 •q3• x^2
Elena, for some reason I'm getting an answer of -3
(8.00 x 10^-12) x (d-x)^2 = (6.00 x 10^-12) x (x^2)
(d-x)^2/x^2 = 7.5 x 10^-1
(d-x)(d-x)/x^2 = 7.50 x 10^-1
x^2-x+0.25/x^2= 7.50 x 10^-1
then I get x = -3
Can you help! I'm not sure where i am going wrong.
q1 • (d-x)^2 = q2 • x^2
4•10^-9•(d-x)^2 = 3•10^-9•x^2
4(d^2 - 2•d•x + x^2) = 3•x^2,
x^2 - 4x + 1 = 0
x =2 ± sqrt(4-1) =2 ± 1.73.
x1 = 0.27 m, x2 =3.73m (falls out)
To find the point between the two charges where the net electrostatic force is zero, we need to calculate the electric field due to each charge and find the point where the two electric fields cancel each other out.
The electric field due to a point charge can be determined using Coulomb's Law:
Electric Field (E) = (k * Q) / r^2,
where k is the Coulomb's constant (8.99 x 10^9 N m^2/C^2), Q is the charge, and r is the distance from the charge.
First, let's calculate the electric field due to the 4.00nC charge at different points along the line between the two charges:
E1 = (8.99 x 10^9 N m^2/C^2 * 4.00 x 10^-9 C) / (0.250 m)^2,
where the distance from the 4.00nC charge is 0.250m.
Next, let's calculate the electric field due to the 3.00nC charge at different points along the line between the two charges:
E2 = (8.99 x 10^9 N m^2/C^2 * 3.00 x 10^-9 C) / (0.250 m)^2,
where the distance from the 3.00nC charge is also 0.250m.
To cancel the net electrostatic force on the 2.00nC charge, the electric field due to the 4.00nC charge (E1) and the electric field due to the 3.00nC charge (E2) must have equal magnitudes but opposite directions. So, we set E1 = -E2:
(8.99 x 10^9 N m^2/C^2 * 4.00 x 10^-9 C) / (0.250 m)^2 = -(8.99 x 10^9 N m^2/C^2 * 3.00 x 10^-9 C) / (0.250 m)^2.
Now, we can solve the equation to find the distance from the 4.00nC charge:
4.00 x 10^-9 / (0.250 m)^2 = -3.00 x 10^-9 / (0.250 m)^2.
Solving for the unknown distance, we get:
4.00 x 10^-9 = -3.00 x 10^-9,
which is not possible. This means there is no point between the two charges where the net electrostatic force on the 2.00nC charge is zero.