Two charges Q 1 =500/mu(C) and Q 2 =100/mu(C) are located on the XY plane at the positions r1=3/vec(j)m and r2=4/vec(i)m. Find the force exerted on the Q2(a)14.4/vec(i)+10.8/vec(j)(b)14.4/vec(i)-10.8/vec(j)N(c)10.8/vec(i)-14.4/vec(j)N(d)10.8/vec(i)+14.4/vec(j)N
To find the force exerted on Q2, we can use Coulomb's law, which states that the force between two charges is given by:
F = (k * |Q1 * Q2|) / r^2
Where:
- F is the magnitude of the force between the charges,
- k is the electrostatic constant (k = 9 * 10^9 N m^2/C^2),
- Q1 and Q2 are the charges,
- |Q1 * Q2| is the product of the magnitudes of the charges,
- r is the distance between the charges.
Let's calculate the force for each option:
(a) To calculate the force at the position (14.4i + 10.8j)N, we need to find the distance between the two charges using the Pythagorean theorem:
r = sqrt((14.4^2) + (10.8^2)) = 18 m
Now, we can calculate the force using Coulomb's law:
F = (9 * 10^9 N m^2/C^2) * ((500 * 10^-6 C) * (100 * 10^-6 C))/(18^2 m^2)
= (9 * 10^9 N m^2/C^2) * (50 * 10^-8 C^2)/(18^2 m^2)
= 0.138 N
(b) Similar to (a), the position (14.4i - 10.8j)N has the same distance of 18 m. Therefore, we can use the same formula with Q2 as -100 * 10^-6 C since it has the opposite sign:
F = (9 * 10^9 N m^2/C^2) * ((500 * 10^-6 C) * (-100 * 10^-6 C))/(18^2 m^2)
= -0.277 N
(c) For the position (10.8i - 14.4j)N, we need to find the distance:
r = sqrt((10.8^2) + (14.4^2)) = 18 m
Using Coulomb's law:
F = (9 * 10^9 N m^2/C^2) * ((500 * 10^-6 C) * (100 * 10^-6 C))/(18^2 m^2)
= 0.138 N
(d) The position (10.8i + 14.4j)N also has the same distance of 18 m. Using Coulomb's law:
F = (9 * 10^9 N m^2/C^2) * ((500 * 10^-6 C) * (100 * 10^-6 C))/(18^2 m^2)
= 0.138 N
Therefore, the correct answer is:
(c) 10.8i - 14.4j N