Two point charges are 10.0 cm apart and have charges of 2.0 µC and -2.0 µC, respectively. What is the magnitude of the electric field at the midpoint between the two charges?

E=2kq/.05^2

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a charge Q1 Lcm away from Q2. At what point on the line joining the two charges the electric field is zero

To find the magnitude of the electric field at the midpoint between the two charges, you can use the equation for the electric field due to a point charge. The equation is given by:

E = k * (Q / r^2)

where,
E is the magnitude of the electric field,
k is the Coulomb's constant (8.99 x 10^9 N m^2/C^2),
Q is the charge, and
r is the distance between the point charge and the location where you want to find the electric field.

In this case, we have two charges, one positive and one negative. At the midpoint, the distance from each charge is the same.

Let's calculate the electric field due to the positive charge:

E1 = k * (Q1 / r^2)

where,
Q1 = 2.0 µC (charge of the positive charge),
r = 5.0 cm (half of the distance between the charges, as the midpoint is halfway between them).

Substituting the values into the equation:

E1 = (8.99 x 10^9 N m^2/C^2) * (2 x 10^-6 C / (0.05 m)^2)

Next, let's calculate the electric field due to the negative charge:

E2 = k * (Q2 / r^2)

where,
Q2 = -2.0 µC (charge of the negative charge).

Again, substituting the values into the equation:

E2 = (8.99 x 10^9 N m^2/C^2) * (-2 x 10^-6 C / (0.05 m)^2)

Since the electric field is a vector quantity, we need to take the vector sum of E1 and E2 at the midpoint. Since the charges are equal in magnitude, the electric fields at the midpoint have the same magnitude but opposite direction. Therefore, the vector sum is simply the difference between their magnitudes:

E_total = |E1 - E2|

Now, you can calculate the magnitude of the electric field at the midpoint by subtracting the two values and taking the absolute value:

E_total = |E1 - E2| = |(8.99 x 10^9 N m^2/C^2) * (2 x 10^-6 C / (0.05 m)^2) - (8.99 x 10^9 N m^2/C^2) * (-2 x 10^-6 C / (0.05 m)^2)|

Simplifying the equation, you can find the magnitude of the electric field at the midpoint between the two charges.

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

Here are the steps to find the magnitude of the electric field at the midpoint:

1. Determine the electric field due to the first charge: The electric field due to a point charge can be calculated using the formula E = k * (Q / r^2), where E is the electric field, k is the electrostatic constant (k = 9.0 x 10^9 N*m^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 first charge, Q1 = 2.0 µC and the distance from the charge to the midpoint is half of the total separation, which is 5.0 cm or 0.05 m. Plugging these values into the formula gives us:

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

2. Determine the electric field due to the second charge: Using the same formula, the electric field due to the second charge can be calculated. For the second charge, Q2 = -2.0 µC, and the distance from the charge to the midpoint is also 5.0 cm or 0.05 m. Plugging these values into the formula gives us:

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

3. Calculate the total electric field at the midpoint: To find the total electric field at the midpoint, we need to add the electric fields due to each charge together. Since the electric field is a vector quantity, we need to consider the direction as well. In this case, the electric fields due to both charges are in the opposite direction and have the same magnitude, so we can subtract them:

E_total = E1 - E2

4. Determine the magnitude of the electric field at the midpoint: Since the electric field is a vector quantity, we need to take the magnitude of the total electric field to answer the question. By removing the negative sign (since the magnitude is always positive), we get the magnitude of the electric field at the midpoint.

Now you can plug in the values and calculate the magnitude of the electric field at the midpoint between the two charges.