To find the magnitude and direction of the electric field created at the position x=4.00 m, we need to calculate the electric field contribution from each point charge and then sum them up.
Let's define the positive direction of the x-axis to be towards the right.
The electric field created by a point charge is given by the equation:
E = k * q / r^2
where:
E is the magnitude of the electric field,
k is Coulomb's constant (k = 9.0 x 10^9 Nm^2/C^2),
q is the charge of the point charge,
r is the distance from the point charge to the point where we want to measure the electric field.
First, let's consider q1 = +4.00 C, which is located at x1 = 1.00 m.
The distance from q1 to the point x = 4.00 m is: r1 = 4.00 m - 1.00 m = 3.00 m.
The electric field created by q1 at x = 4.00 m is:
E1 = k * q1 / r1^2 = (9.0 x 10^9 Nm^2/C^2) * (4.00 C) / (3.00 m)^2
Next, let's consider q2 = -3.00 C, which is located at x2 = -2.00 m.
The distance from q2 to the point x = 4.00 m is: r2 = 4.00 m - (-2.00 m) = 6.00 m.
The electric field created by q2 at x = 4.00 m is:
E2 = k * q2 / r2^2 = (9.0 x 10^9 Nm^2/C^2) * (-3.00 C) / (6.00 m)^2
Finally, let's consider q3 = +2.00 C, which is located at x3 = 6.00 m.
The distance from q3 to the point x = 4.00 m is: r3 = 4.00 m - 6.00 m = -2.00 m.
The electric field created by q3 at x = 4.00 m is:
E3 = k * q3 / r3^2 = (9.0 x 10^9 Nm^2/C^2) * (2.00 C) / (-2.00 m)^2
Now, we can sum up the electric fields created by each charge:
E_total = E1 + E2 + E3
Calculate the magnitudes and directions of E1, E2, and E3 using the given values of q1, q2, q3, and the equations above.
Three point charges lie on the x-axis as shown. What is the magnitude and direction of the electric field created at the position x=4.00 m by these charges?
q1= +4.00 C
q2=-3.00 C
q3= +2.00 C
1 answer