Electric Field of Two Charges : 15.0 points
A point charge is located at x=0, and a point charge is placed at on the -axis of a cartesian coordinate system.The goal of this problem is to determine the electric field, , at various points along the -axis.
(a)What is (in N/C) for -68.0 m ?
unanswered
What is (in N/C) at -0.42 m?
unanswered
What is (in N/C) at 65 m?
unanswered
(b) At what point (apart from ), is ? Express your answer in meters.
To solve this problem, we need to use the formula for the electric field due to a point charge, which is given by:
E = k * (Q / r^2)
where E is the electric field, k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), Q is the charge of the point charge, and r is the distance between the point charge and the point where we want to calculate the electric field.
(a) To find the electric field at -68.0 m, we need to calculate the individual electric field contributions from both charges and then sum them up. Let's assume that the charge at x = 0 is Q1 and the charge at x = 0.42 m is Q2.
The electric field due to Q1 at -68.0 m can be calculated using the formula:
E1 = k * (Q1 / r1^2)
where r1 is the distance between Q1 and -68.0 m. Since Q1 is located at x = 0, the distance r1 is simply the absolute value of -68.0 m, which is 68.0 m.
Similarly, the electric field due to Q2 at -68.0 m can be calculated using the formula:
E2 = k * (Q2 / r2^2)
where r2 is the distance between Q2 and -68.0 m. Since Q2 is located at x = 0.42 m, the distance r2 is the absolute value of 0.42 m plus 68.0 m.
Once you calculate E1 and E2, you can add them together to get the total electric field E at -68.0 m.
(b) To find the point (apart from x = 0) where the electric field is zero (E = 0), we need to equate the electric field contributions from both charges. So we have:
k * (Q1 / r1^2) = k * (Q2 / r2^2)
Simplifying the equation, we can solve for r2 in terms of r1:
(Q1 / r1^2) = (Q2 / r2^2)
r2^2 = (Q2 / Q1) * r1^2
Taking the square root of both sides, we get:
r2 = sqrt((Q2 / Q1) * r1^2)
Thus, r2 is the distance from Q2 to the point where the electric field is zero, apart from x = 0.
By using these formulas and the given values of charges and distances, you can calculate the electric field and the point where it is zero.