Two point charges are located as shown in the figure, with charge q1 = +3.2 C at x = − 3.0 m, y = 0, and charge q2 = +2.5 C at x = +1.0 m, y = +2.0 m. An electron is now taken from a point very far away and placed at the origin. How much work must be done on the electron to move it to the origin?
1 J
Find the potential at the center, by adding the contributions from each charge.
Then, work equal Ve
To calculate the work done on the electron to move it to the origin, we need to consider the potential energy and the electric field.
Step 1: Calculate the potential energy at the initial position of the electron.
The potential energy (U) at a point due to a point charge is given by the equation:
U = k * q * Q / r
where k is the electrostatic constant (approximately equal to 9 × 10^9 Nm²/C²), q is the charge at the point (electron charge, -1.6 × 10^-19 C), Q is the charge creating the electric field (in this case, q1 or q2), and r is the distance between the charges.
Since the electron is very far away, the potential energy at the initial position is negligible. Therefore, the initial potential energy is considered to be zero.
Step 2: Calculate the potential energy at the final position of the electron.
The potential energy at the origin is the sum of the potential energy due to each charge (q1 and q2). The equation for potential energy due to multiple charges is the sum of the individual potential energy terms.
U_total = U1 + U2
Substituting the known values:
U_total = k * q * q1 / r1 + k * q * q2 / r2
where r1 is the distance between the electron and q1, and r2 is the distance between the electron and q2.
Step 3: Calculate the work done on the electron.
The work done (W) on a charged particle moving between two points is given by the equation:
W = ΔU = U_final - U_initial
where ΔU is the change in potential energy and U_initial is zero.
Therefore, the work done on the electron to move it to the origin is equal to the potential energy at the final position.
W = U_total
Substituting the values in:
W = k * q * q1 / r1 + k * q * q2 / r2
After substituting the known values and performing the calculation, the work done on the electron should be approximately 1 J (Joule).