Two charges of magnitude +2×10^–6 C each are 60cm apart. find the magnitude of the force exerted by these charges on a third charge of magnitude +4×10^-4C that is 50cm away from each of the charge.
To find the magnitude of the force exerted by the two charges on the third charge, we can use Coulomb's Law.
Coulomb's Law states that the force (F) between two charged objects is directly proportional to the product of their charges (q1 and q2) and inversely proportional to the square of the distance (r) between them.
Mathematically, Coulomb's Law is represented as:
F = k * (|q1| * |q2|) / r^2
Where:
F is the magnitude of the force between the charges
k is the Coulomb's constant (k = 9 × 10^9 Nm^2/C^2)
|q1| and |q2| are the magnitudes of the charges
r is the distance between the charges
In this case, we have two charges of magnitude +2×10^-6 C each and a third charge of magnitude +4×10^-4 C. The distance between the third charge and the other two charges is 50 cm (0.5 m).
Let's substitute the given values into the Coulomb's Law equation:
F = (9 × 10^9 Nm^2/C^2) * [(|q1| * |q2|) / r^2]
F = (9 × 10^9 Nm^2/C^2) * [((2×10^-6 C) * (2×10^-6 C)) / (0.5 m)^2]
Now, let's calculate the force using this equation:
F = (9 × 10^9 Nm^2/C^2) * [(4×10^-12 C^2) / (0.5)^2]
F = (9 × 10^9 Nm^2/C^2) * (4×10^-12 C^2) / 0.25
F = 144 × 10^-3 N
F = 1.44 × 10^-1 N
F = 0.144 N
Therefore, the magnitude of the force exerted by the two charges on the third charge is 0.144 Newtons.