What is the magnitude of the electric field midway between two point charges, -16.4 μC and +11.0 μC, that are 8.95 cm apart?
To find the magnitude of the electric field midway between two point charges, you can make use of the equation for the electric field due to a point charge. The electric field due to a point charge is given by the equation:
E = k * (q / r^2)
where E is the electric field, k is Coulomb's constant (k = 8.99 x 10^9 N m²/C²), q is the charge of the point charge, and r is the distance from the point charge.
In this case, we have two point charges: -16.4 μC and +11.0 μC. Since the charges are opposite in sign, their electric fields will have opposite directions. At the midpoint between the charges, the electric fields will cancel each other out in the horizontal direction, leaving only the vertical components to contribute to the net electric field.
First, let's calculate the electric fields due to each point charge individually at the midpoint. The distance is given as 8.95 cm, which is 0.0895 meters. Plugging in these values into the equation, we get:
E1 = k * (q1 / r^2) = (8.99 x 10^9 N m²/C²) * (-16.4 x 10^-6 C) / (0.0895 m)^2
E2 = k * (q2 / r^2) = (8.99 x 10^9 N m²/C²) * (11.0 x 10^-6 C) / (0.0895 m)^2
Next, add up the vertical components of the electric fields:
E_net = E2 - E1
Finally, calculate the magnitude of the net electric field by taking the absolute value of E_net:
|E_net| = |E2 - E1|
This will give you the magnitude of the electric field midway between the two point charges.