What is the potential halfway between two point charges spaced 1 mm apart if q1=10 micro coulumbs and q2= -5 micro coulumbs?
To find the potential halfway between two point charges, we can use the formula for the potential due to a point charge:
V = (k * q) / r
where V is the potential, k is the Coulomb's constant (8.99 × 10^9 N m^2/C^2), q is the charge, and r is the distance from the charge.
In this case, we have two point charges q1 = 10 μC and q2 = -5 μC spaced 1 mm (or 0.001 m) apart. We need to calculate the potential halfway between them.
First, let's calculate the potential due to q1 at the halfway point:
V1 = (k * q1) / r1
where r1 is the distance from q1 to the halfway point.
Since the charges are symmetrically placed with respect to the halfway point, r1 = r2 = 0.001 m / 2 = 0.0005 m.
Plugging in the values, we get:
V1 = (8.99 × 10^9 N m^2/C^2 * 10 × 10^-6 C) / 0.0005 m
Now let's calculate the potential due to q2 at the halfway point:
V2 = (k * q2) / r2
Plugging in the values:
V2 = (8.99 × 10^9 N m^2/C^2 * -5 × 10^-6 C) / 0.0005 m
Finally, we can find the potential halfway between the charges by summing the potentials due to each charge:
V = V1 + V2
Evaluate the expression to find the numerical value of V.