The drawing shows three point charges fixed in place. The charge at the coordinate origin has a value of q1 = +8.70 µC; the other two charges have identical magnitudes, but opposite signs: q2 = -4.50 µC and q3 = +4.50 µC.
Determine the net force (magnitude and direction) exerted on q1 by the other two charges.
If q1 had a mass of 1.62 g and it were free to move, what would be its acceleration?
To determine the net force exerted on q1 by the other two charges, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
1. First, calculate the individual forces between q1 and q2 as well as between q1 and q3.
The formula to calculate the force F between two charges is:
F = k * (q1 * q2) / r^2
where k is the electrostatic constant (9 × 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Given that q1 = +8.70 µC (microcoulombs) = 8.70 × 10^-6 C,
and q2 = -4.50 µC = -4.50 × 10^-6 C,
and r1 = distance between q1 and q2.
Calculate the force F1 between q1 and q2 using Coulomb's Law.
2. Next, calculate the force between q1 and q3.
Given that q1 = +8.70 µC (microcoulombs) = 8.70 × 10^-6 C,
and q3 = +4.50 µC = 4.50 × 10^-6 C,
and r2 = distance between q1 and q3.
Calculate the force F2 between q1 and q3 using Coulomb's Law.
3. Finally, find the net force (magnitude and direction) exerted on q1 by the other two charges.
Since q2 and q3 have opposite signs, their forces will have opposite directions. The net force will be the vector sum of F1 and F2, i.e., F_net = F1 + F2.
Determine the magnitude and direction of the net force F_net.
The direction will be the direction of the resultant force vector.
Moving on to the second part,
4. To determine the acceleration of q1 if it were free to move, we need to use Newton's second law of motion.
Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
F = m * a
F is the net force calculated in the previous step, m is the mass of q1, and a is the acceleration.
Given that mass of q1 = 1.62 g = 0.00162 kg,
Calculate the acceleration a using Newton's second law.
a = F_net / m
where F_net is the net force calculated earlier.
By following these steps, you can determine the net force exerted on q1 by the other two charges and calculate its acceleration if it were free to move.