The electric field midway between two equal but opposite point charges is 1000 N/C, and the distance between the charges is 16.0 cm. What is the magnitude of the charge on each?
To find the magnitude of the charge on each point charge, we can use the formula for the electric field due to a point charge:
E = k * (|q1| / r1^2)
Where:
- E is the electric field
- k is the Coulomb's constant, approximately equal to 9 * 10^9 N m^2 / C^2
- |q1| is the magnitude of the charge on the point charge
- r1 is the distance from the point charge to the location where we want to find the electric field
Given that the electric field midway between the charges is 1000 N/C and the distance between the charges is 16.0 cm, we know that the electric field at this location is due to both point charges. Since the charges are equal but opposite, the electric field contributions from each charge add up.
The distance between the charges is 16.0 cm, so the distance from each charge to the midpoint is half of that, or 8.0 cm. We can convert this to meters by dividing by 100:
r1 = 8.0 cm / 100 = 0.08 m
The electric field at the midpoint is given as 1000 N/C. Since the electric field adds up for both point charges, we can write:
E_total = E1 + E2
Substituting the formula for the electric field, we have:
1000 N/C = k * (|q1| / r1^2) + k * (|q2| / r2^2)
Since the charges are equal in magnitude, we can write:
1000 N/C = k * (2 * |q1| / r1^2)
Simplifying further:
|q1| = (1000 N/C) * (r1^2) / (2 * k)
Now we can substitute the known values:
|q1| = (1000 N/C) * (0.08 m)^2 / (2 * 9 * 10^9 N m^2 / C^2)
Calculating this expression:
|q1| ≈ 3.56 * 10^-8 C
Therefore, the magnitude of the charge on each point charge is approximately 3.56 * 10^-8 C.