a point charge of -4.00nc is the origin, and a second point charge of +6.00nc is on the x axis at x=0.800m. Find the magnitude and directin of the electric field at each of the following points on the x asix : a) x =20.0 cm b) x=1.20 m c) x = -20.0 cm

sketch the diagram. Notice the E field points toward the negative charge due to the negative charge, and away from the + charge due to it. In between x=0 and x=.8, they both point toward the negative charge.

E= 131 N/C

E= 131 N/C

θ = 12.6 ∘ up from the negative x axis

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To find the magnitude and direction of the electric field at a certain point on the x-axis, we can use the formula for electric field due to a point charge.

The formula for electric field due to a point charge is given as:

E = k * (q / r^2)

Where:
- E is the magnitude of the electric field
- k is the Coulomb's constant which is equal to 9.0 * 10^9 Nm^2/C^2
- q is the charge of the point charge
- r is the distance between the point charge and the point where we want to find the electric field

Let's calculate the magnitude and direction of the electric field at each point:

a) x = 20.0 cm (0.20 m)
- The distance, r, is the difference between the point charge position and the point where we want to find the electric field.
- r = 0.20 m
- Plugging the values into the formula:

E = (9.0 * 10^9 Nm^2/C^2) * (-4.00 * 10^-9 C) / (0.20)^2
E = (-1.8 * 10^6 N/C)

The magnitude of the electric field at x = 20.0 cm is 1.8 * 10^6 N/C, directed towards the negative x-axis.

b) x = 1.20 m
- The distance, r, is the difference between the point charge position and the point where we want to find the electric field.
- r = 1.20 m
- Plugging the values into the formula:

E = (9.0 * 10^9 Nm^2/C^2) * (-4.00 * 10^-9 C) / (1.20)^2
E = (-2.08 * 10^5 N/C)

The magnitude of the electric field at x = 1.20 m is 2.08 * 10^5 N/C, directed towards the negative x-axis.

c) x = -20.0 cm (-0.20 m)
- The distance, r, is the difference between the point charge position and the point where we want to find the electric field.
- r = -0.20 m (Note: the distance is negative because the point is on the opposite side of the origin compared to the point charge)
- Plugging the values into the formula:

E = (9.0 * 10^9 Nm^2/C^2) * (-4.00 * 10^-9 C) / (-0.20)^2
E = (1.8 * 10^6 N/C)

The magnitude of the electric field at x = -20.0 cm is 1.8 * 10^6 N/C, directed towards the negative x-axis.