A point charge of -4.00nC is at the origin, and a second point charge of 6.00nC is on the axis at x = 0.800m . Find the magnitude and direction of the electric field at each of the following points on the axis. x_2 = 17.0cm, x_3 = 1.30m , x_4=-17.0cm
To find the magnitude and direction of the electric field at each point on the axis, we can use the formula for the electric field due to a point charge:
Electric field (E) = (k * q) / r^2
where k is Coulomb's constant (8.99 × 10^9 Nm^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.
Let's calculate the electric field at each given point step by step:
1. Electric field at point x_2 = 17.0 cm:
First, we need to convert the distance from centimeters to meters:
x_2 = 17.0 cm = 17.0 * 10^(-2) m = 0.17 m
Now we can use the formula for the electric field:
E_2 = (k * q) / r^2
E_2 = (8.99 × 10^9 Nm^2/C^2) * (-4.00 × 10^(-9) C) / (0.17 m)^2
Calculating this expression gives us:
E_2 = -7.02 × 10^4 N/C
So, the magnitude of the electric field at point x_2 is 7.02 × 10^4 N/C, and the direction is negative along the negative x-axis.
2. Electric field at point x_3 = 1.30 m:
Using the same formula:
E_3 = (k * q) / r^2
E_3 = (8.99 × 10^9 Nm^2/C^2) * (-4.00 × 10^(-9) C) / (1.30 m)^2
Calculating this expression gives us:
E_3 = -2.45 × 10^4 N/C
So, the magnitude of the electric field at point x_3 is 2.45 × 10^4 N/C, and the direction is negative along the negative x-axis.
3. Electric field at point x_4 = -17.0 cm:
First, we need to convert the distance from centimeters to meters:
x_4 = -17.0 cm = -17.0 * 10^(-2) m = -0.17 m
Now we can use the formula for the electric field:
E_4 = (k * q) / r^2
E_4 = (8.99 × 10^9 Nm^2/C^2) * (-4.00 × 10^(-9) C) / (0.17 m)^2
Calculating this expression gives us:
E_4 = 7.02 × 10^4 N/C
So, the magnitude of the electric field at point x_4 is 7.02 × 10^4 N/C, and the direction is positive along the positive x-axis.
To find the magnitude and direction of the electric field at each point on the x-axis, we can use Coulomb's Law, which states that the electric field produced by a point charge is given by:
E = k * (|q1| / r^2)
where E is the electric field, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), |q1| is the magnitude of the point charge, and r is the distance between the point charge and the point where we want to find the electric field.
Let's calculate the electric field at each of the given points on the x-axis:
1. Point P1: x1 = 17.0 cm = 0.17 m
To find the electric field at P1 due to the point charge at the origin, we need to calculate the distance between them. Since one charge is at the origin (x=0) and the other is at x=0.17 m, the distance between them is 0.17 m. Substituting these values into the equation, we get:
E1 = k * (|q1| / r^2)
= (9 x 10^9 Nm^2/C^2) * (4.00 x 10^-9 C) / (0.17 m)^2
Calculating the above expression gives us the magnitude of the electric field at P1. To determine the direction, we need to consider the signs of the charges. The negative charge at the origin produces an electric field directed towards itself, while the positive charge on the x-axis produces an electric field that points in the opposite direction. Therefore, the electric field at P1 is directed towards the negative charge at the origin.
2. Point P2: x2 = 1.30 m
To find the electric field at P2 due to the point charges, we again need to calculate the distance between them. Since one charge is at the origin (x=0) and the other is at x=1.30 m, the distance between them is 1.30 m. Plugging in the values into the equation, we get:
E2 = k * (|q1| / r^2)
= (9 x 10^9 Nm^2/C^2) * (4.00 x 10^-9 C) / (1.30 m)^2
Calculating the above expression gives us the magnitude of the electric field at P2. The direction of the electric field at P2 is towards the negative charge at the origin.
3. Point P3: x3 = -17.0 cm = -0.17 m
To find the electric field at P3, we need to calculate the distance between P3 and the point charge at the origin. Since one charge is at the origin (x=0) and the other is at x=-0.17 m, the distance between them is 0.17 m. Plugging in the values into the equation, we get:
E3 = k * (|q1| / r^2)
= (9 x 10^9 Nm^2/C^2) * (4.00 x 10^-9 C) / (0.17 m)^2
Calculating the above expression gives us the magnitude of the electric field at P3. The direction of the electric field at P3 is away from the negative charge at the origin.
Therefore, the magnitude and direction of the electric field at each of the given points on the x-axis are as follows:
- At P1: magnitude = E1, direction = towards the negative charge at the origin
- At P2: magnitude = E2, direction = towards the negative charge at the origin
- At P3: magnitude = E3, direction = away from the negative charge at the origin