Two particles are fixed to an x axis: particle 1 of charge q1 = 2.22 x 10-8 C at x = 15.6 cm and particle 2 of charge q2 = -4.33q1 at x = 66.7 cm. At what coordinate on the x axis is the electric field produced by the particles equal to zero?
To find the coordinate on the x-axis where the electric field produced by the particles is equal to zero, we need to use the concept of superposition. The electric field produced by each particle can be calculated using the formula:
E = k * (q / r^2)
Where:
E = electric field
k = electrostatic constant (8.99 x 10^9 Nm^2/C^2)
q = charge of the particle
r = distance from the particle
Since we are looking for the position where the net electric field is zero, we need to consider the electric field contributions from both particles. Assuming the positive direction of the x-axis is to the right, the electric field produced by particle 1 at a point x is given by:
E1 = k * (q1 / (x - x1)^2)
And the electric field produced by particle 2 at the same point x is given by:
E2 = k * (q2 / (x - x2)^2)
To find the value of x where the total electric field is zero (E = E1 + E2 = 0), we can set up the equation,
E1 + E2 = 0
k * (q1 / (x - x1)^2) + k * (q2 / (x - x2)^2) = 0
Substituting the known values, we have:
(8.99 x 10^9 Nm^2/C^2) * (2.22 x 10^-8 C / (x - 15.6 cm)^2) + (8.99 x 10^9 Nm^2/C^2) * (-4.33 * 2.22 x 10^-8 C / (x - 66.7 cm)^2) = 0
Simplifying the equation and solving for x will give us the desired coordinate on the x-axis where the electric field produced by the particles is zero.