A point charge of -4.00 is at the origin, and a second point charge of 6.00 is on the axis at = 0.850 . Find the magnitude and direction of the electric field at each of the following points on the axis.
a) x=25.0cm
b) x=1.10m
c) x=-15.0cm
To find the magnitude and direction of the electric field at a given point, we can use the principle of superposition. According to this principle, the total electric field at a point due to multiple charges is the vector sum of the electric fields created by each individual charge.
In this case, we have two point charges: one at the origin with a charge of -4.00 and another one on the axis at x = 0.850 with a charge of 6.00. We will consider the positive x-axis as the forward direction and the negative x-axis as the backward direction.
a) To find the electric field at x = 25.0 cm (or 0.25 m), we need to calculate the electric field created by each point charge separately and then add them together.
The electric field created by a point charge q at a distance r from the charge is given by Coulomb's Law:
E = k * (q / r^2)
Where:
E is the electric field,
k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2),
q is the charge, and
r is the distance from the charge to the point where we want to calculate the electric field.
For the charge at the origin (-4.00), the distance to the desired point is 0.25 m. Plugging these values into the formula, we get:
E1 = (9 x 10^9) * (-4.00) / (0.25^2) N/C
For the charge at x = 0.850 (6.00), the distance to the desired point is 0.250 - 0.850 = 0.600 m. Plugging these values into the formula, we get:
E2 = (9 x 10^9) * (6.00) / (0.600^2) N/C
Adding these two electric field values together gives us the total electric field at x = 0.25 m.
b) To find the electric field at x = 1.10 m, we repeat the same process as in part (a), using the updated distance value.
c) To find the electric field at x = -15.0 cm (or -0.15 m), we again use the same process as in part (a), but this time we will need to consider the direction of the electric field due to the negative charge at the origin. The electric field should point towards the charge, which in this case would be in the positive x-direction.
By calculating the electric field at these three points using the above steps, you can find the magnitude and direction of the electric field created by the given charges at each location on the axis.