The electric field at the point x = 5.00cm and y = 0 points in the positive x direction with a magnitude of 10.0 N/C. At the point x = 10.0cm and y = 0 the electric field points in the positive x direction with a magnitude of 16.0 N/C. Assume this electric field is produced by a single point charge.
A)Find the charge's location.
B)Find the sign of the charge.
positive
negative
C)Find the magnitude of the charge in pC.
To solve this problem, we can use the formula for the electric field produced by a point charge:
E = kq / r^2
Where:
E is the electric field
k is Coulomb's constant (8.99 x 10^9 N m^2 / C^2)
q is the charge
r is the distance from the charge to the point where we are measuring the electric field
We have two points where we know the electric field magnitude and direction. Let's consider the first point (x = 5.00 cm, y = 0) and the second point (x = 10.0 cm, y = 0). At both points, the electric field points in the positive x direction.
A) To find the charge's location, we need to determine the distance between the two points. In this case, since both points are on the x-axis, the distance between them is simply the difference in their x-coordinates:
Δx = 10.0 cm - 5.00 cm = 5.00 cm
Since both points are on the same side of the origin, we can infer that the charge is located between these two points. Therefore, the charge's location is at x = 7.5 cm.
B) To find the sign of the charge, we need to consider the direction of the electric field. In this case, since the electric field points in the positive x direction at both points, we can conclude that the charge is positive.
C) To find the magnitude of the charge in pC, we can use the equation:
E = kq / r^2
First, let's convert the distances to meters:
Δx = 5.00 cm = 0.050 m
We can rearrange the equation to solve for q:
q = Er^2 / k
Substituting the known values:
E = 10.0 N/C
r = Δx = 0.050 m
k = 8.99 x 10^9 N m^2 / C^2
q = (10.0 N/C) * (0.050 m)^2 / (8.99 x 10^9 N m^2 / C^2)
Simplifying the expression, we find:
q ≈ 2.86 x 10^-9 C
To convert the charge to pC, we can multiply it by 10^12:
q ≈ 2.86 x 10^3 pC
So the magnitude of the charge is approximately 2.86 x 10^3 pC.