A point charge of +10 micro-coulombs lies at x = -0.39 m, y = 0 m, a point charge of -5.7 micro-coulombs lies at x = +0.39 m, y = 0 m, and a point charge of +14.9 micro-coulombs lies at x = 0 m, y = -0.3 m. A point charge of +10 micro-coulombs is moves from x = 0 m, y = +0.11 m to x = 0 m, y = +0.54 m. How much does the kinetic energy of the charge which is moved change in Joules?
To calculate the change in kinetic energy of a charged particle, we need to determine the initial and final velocities of the particle.
Given that the charge is moving from (0 m, 0.11 m) to (0 m, 0.54 m), we can calculate the change in y-coordinate as:
Δy = 0.54 m - 0.11 m = 0.43 m
The change in kinetic energy can be calculated as:
ΔK.E. = (1/2)mv_f^2 - (1/2)mv_i^2
To find the initial and final velocities, we need to calculate the electric potential energy. Electric potential energy is given by the formula:
PE = k * (|q1 * q2| / r)
where k is the Coulomb's constant (9 x 10^9 N*m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Let's consider the electric potential energy for the initial and final positions.
Initial position:
The electric potential energy between the charge at (0 m, 0.11 m) and the other charges can be calculated as:
PE_initial = k * |q1 * q2| / r1 + k * |q3 * q4| / r2
where r1 is the distance between the charges (0.39 m), r2 is the distance between the charges (0.41 m), q1 and q2 are the charges (-5.7 μC and 10 μC), q3 and q4 are the charges (-5.7 μC and 14.9 μC), and k is the Coulomb's constant.
Calculating PE_initial:
PE_initial = - (9 x 10^9 N*m^2/C^2) * [(5.7 x 10^-6 C) * (10 x 10^-6 C) / 0.39 m] + (9 x 10^9 N*m^2/C^2) * [(5.7 x 10^-6 C) * (14.9 x 10^-6 C) / 0.41 m]
Similarly, we can calculate the electric potential energy at the final position, PE_final.
Final position:
The electric potential energy between the charge at (0 m, 0.54 m) and the other charges can be calculated as:
PE_final = k * |q1 * q2| / r1 + k * |q3 * q4| / r2
where r1 is the distance between the charges (0.39 m), r2 is the distance between the charges (0.41 m), q1 and q2 are the charges (-5.7 μC and 10 μC), q3 and q4 are the charges (-5.7 μC and 14.9 μC), and k is the Coulomb's constant.
Calculating PE_final:
PE_final = (9 x 10^9 N*m^2/C^2) * [(5.7 x 10^-6 C) * (10 x 10^-6 C) / 0.39 m] + (9 x 10^9 N*m^2/C^2) * [(5.7 x 10^-6 C) * (14.9 x 10^-6 C) / 0.41 m]
Finally, the change in kinetic energy can be calculated:
ΔK.E. = PE_final - PE_initial
I cannot provide the exact numerical value without knowing the values of the charges and distances since they are missing in the question. However, by substituting the values, you can calculate the change in kinetic energy using the mentioned formulas.