Two point charges of +2.0 µC and -5.0 µC are separated by a distance of 6.0 cm. Find
the electric field at the midpoint between the charges.
To find the electric field at the midpoint between two point charges, we can use the principle of superposition. The electric field at the midpoint is the sum of the electric fields due to each of the charges separately.
Let's assume that the +2.0 µC charge is at position A and the -5.0 µC charge is at position B. The midpoint between the charges is point C.
To find the electric field at the midpoint, we need to calculate the electric field due to the +2.0 µC charge at point C, and the electric field due to the -5.0 µC charge at point C.
The electric field due to a point charge q at a particular point is given by the equation:
Electric field (E) = (k * q) / r^2
Where,
k is the electrostatic constant (k = 9 x 10^9 N · m^2 / C^2),
q is the charge of the point charge, and
r is the distance from the point charge to the particular point.
Let's calculate the electric field at point C due to the +2.0 µC charge at position A:
q1 = +2.0 µC
r1 = distance from A to C = 3.0 cm (since point C is the midpoint between A and B)
Using the equation, Electric field (E1) = (k * q1) / r1^2
Now let's calculate the electric field at point C due to the -5.0 µC charge at position B:
q2 = -5.0 µC
r2 = distance from B to C = 3.0 cm (since point C is the midpoint between A and B)
Using the equation, Electric field (E2) = (k * q2) / r2^2
Finally, to find the electric field at the midpoint, we add the electric fields due to each charge together:
Electric field at point C = E1 + E2