a) What is the magnitude of the electric field at a point midway between a −8.5μC and a +8.5μC charge 8.0cm apart? Assume no other charges are nearby.

b) What is the direction of the electric field?

To find the magnitude of the electric field at the midpoint between two charges, you can use the formula:

E = k * |q1 - q2| / r^2

Where:
- E is the electric field,
- k is Coulomb's constant (9 * 10^9 Nm^2/C^2),
- q1 and q2 are the charges,
- r is the distance between the charges.

a) Let's calculate the magnitude of the electric field at the midpoint between the charges:

E = (9 * 10^9 Nm^2/C^2) * |(-8.5μC) - (+8.5μC)| / (0.08m)^2
E = (9 * 10^9 Nm^2/C^2) * |(-8.5 * 10^-6 C) - (+8.5 * 10^-6 C)| / (0.08m)^2
E = (9 * 10^9 Nm^2/C^2) * |(-8.5 * 10^-6 C) - (+8.5 * 10^-6 C)| / (0.08m)^2
E = (9 * 10^9 Nm^2/C^2) * |0| / (0.08m)^2
E = 0 N/C

Therefore, the magnitude of the electric field at the midpoint is 0 N/C.

b) Since the magnitude is 0 N/C, the direction of the electric field at the midpoint between the charges is undefined or zero.

To find the magnitude of the electric field at a point midway between two charges, you can use the formula for electric field:

E = k * q / r^2

where E is the electric field, k is the electrostatic constant (k = 9 × 10^9 Nm^2/C^2), q is the charge, and r is the distance between the charges.

a) Here's how you can find the magnitude of the electric field at a point midway between a −8.5μC and a +8.5μC charge 8.0cm apart:

1. Convert the charges to Coulombs: 1 μC = 1 × 10^-6 C
So, -8.5μC = -8.5 × 10^-6 C and +8.5μC = +8.5 × 10^-6 C

2. Calculate the distance between the charges:
r = 8.0 cm = 8.0 × 10^-2 m

3. Substitute the values into the formula and calculate the electric field:
E = (9 × 10^9 Nm^2/C^2) * ((-8.5 × 10^-6 C) + (8.5 × 10^-6 C)) / (8.0 × 10^-2 m)^2

Simplifying the expression, we find:
E = (9 × 10^9 Nm^2/C^2) * (0 C) / (8.0 × 10^-2)^2
E = 0 N/C

Therefore, the magnitude of the electric field at a point midway between the charges is 0 N/C.

b) The direction of the electric field can be determined by the sign of the charges. Since one charge is positive and the other is negative, the electric field created by the positive charge points away from it, while the electric field created by the negative charge points towards it. As the charges have equal magnitudes, the magnitudes of the electric field due to each charge are the same.

Therefore, at the midpoint between the charges, the electric fields due to the positive and negative charges cancel out, resulting in a net electric field of 0 N/C. Hence, the direction of the electric field is zero or undefined at that point.

This one is bookwork. Google "Electric field generated by two point charges utexas" and the first link will help.