Determine the magnitude and direction of an electric field midway between two point charges of 1.2 μC and −2.4 μC that are situated 0.8 cm apart in a vacuum

To solve this problem, we need to use Coulomb's Law, which states that the electric field (E) created by a charge (q) is given by:

E = k*q/r^2

where k is Coulomb's constant (910^9 Nm^2/C^2), q is the charge, and r is the distance from the charge.

First, we need to convert the charges from μC to C (Coulombs) and the distance from cm to m:

q1 = 1.210^-6 C q2 = -2.410^-6 C d = 0.8*10^-2 m

The distance from each charge to the midpoint is d/2 = 0.4*10^-2 m.

Next, we calculate the electric field created by each charge at the midpoint:

E1 = kq1/(d/2)^2 E2 = kq2/(d/2)^2

The total electric field at the midpoint is the vector sum of E1 and E2. Since the charges have opposite signs, their electric fields at the midpoint are in opposite directions. Therefore, we subtract the magnitude of E2 from E1:

E_total = E1 - E2

Finally, the direction of the electric field is from the positive charge to the negative charge.