two point charges are 10.0 cm apart and have chargeso of 2.0 uC (micro)and -2 uC, respectively. What is the magnitude of the electric field at the midpoint between the two charges?

i think the answr is zero..

but i don't understand how to get to it...can you please show me in clear steps how to solve for this...please. i don't understand the way my teacher showed it., pleae show me in steps with explanation. thank you a lot

Definitely not zero. The E contribution from each charge points in the same direction, not in opposite.

Isn't E=kq/r^2, so you double it, and point it toward the negative charge?

but i checked and it does point in the opposite direction

the charges are differnect signs.....

i'm confused!

To find the magnitude of the electric field at the midpoint between the two charges, you can use Coulomb's Law. Coulomb's Law states that the electric field between two point charges is given by the equation:

E = k * (|q1| + |q2|) / r^2

where E is the electric field, k is Coulomb's constant (9 x 10^9 Nm^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.

In this case, the charges are -2.0 uC and +2.0 uC, and the distance between them is 10.0 cm.

Let's calculate the electric field at the midpoint using the steps below:

Step 1: Convert the charges to coulombs.
|q1| = 2.0 uC = 2.0 x 10^(-6) C
|q2| = -2.0 uC = -2.0 x 10^(-6) C

Step 2: Convert the distance to meters.
r = 10.0 cm = 10.0 x 10^(-2) m

Step 3: Substitute the values into the equation.
E = (9 x 10^9 Nm^2/C^2) * (|q1| + |q2|) / r^2
= (9 x 10^9 Nm^2/C^2) * (2.0 x 10^(-6) C - 2.0 x 10^(-6) C) / (10.0 x 10^(-2) m)^2

Step 4: Simplify the equation.
E = 0 N/C

Therefore, the magnitude of the electric field at the midpoint between the two charges is zero.

To find the magnitude of the electric field at the midpoint between the two charges, we can use the principle of superposition. The electric field at a point due to multiple charges is the vector sum of the electric fields produced by each individual charge.

In this case, we have two charges: one with a charge of +2.0 uC and the other with a charge of -2.0 uC. The charges are 10.0 cm apart, so the distance between them is 10.0 cm / 2 = 5.0 cm (since we are considering the midpoint).

Let's break down the problem into steps:

Step 1: Calculate the electric field due to the +2.0 uC charge at the midpoint.
To calculate the electric field due to a point charge, we can use Coulomb's law:

Electric Field (E) = (k * Q) / (r^2)

where
- k is the electrostatic constant (k = 9.0 x 10^9 Nm^2/C^2)
- Q is the charge (in this case, +2.0 uC = 2.0 x 10^-6 C)
- r is the distance between the charge and the point where we want to find the electric field (in this case, 5.0 cm = 0.05 m)

Plugging in the values:

E1 = (9.0 x 10^9 Nm^2/C^2 * 2.0 x 10^-6 C) / (0.05 m)^2
= 7200 N/C

Step 2: Calculate the electric field due to the -2.0 uC charge at the midpoint.
Using the same formula for the electric field:

E2 = (k * Q) / (r^2)

where
- k is the electrostatic constant (k = 9.0 x 10^9 Nm^2/C^2)
- Q is the charge (in this case, -2.0 uC = -2.0 x 10^-6 C)
- r is the distance between the charge and the point where we want to find the electric field (in this case, 5.0 cm = 0.05 m)

Plugging in the values:

E2 = (9.0 x 10^9 Nm^2/C^2 * -2.0 x 10^-6 C) / (0.05 m)^2
= -7200 N/C

Step 3: Calculate the total electric field at the midpoint by adding the two individual electric fields.

E_total = E1 + E2
= 7200 N/C - 7200 N/C
= 0 N/C

Therefore, the magnitude of the electric field at the midpoint between the two charges is zero. This means that the electric forces from the positive and negative charges cancel out and result in no net electric field.