Two stationary point charges of 5.00 and 2.00 are separated by a distance of 60.0 . An electron is released from rest at a point midway between the charges and moves along the line connecting them. What is the electric potential energy of the electron when it is at the midpoint? 14.0 from the 5.00 charge?
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To find the electric potential energy of the electron at the midpoint, we can use the equation:
PE = q * V
where PE is the electric potential energy, q is the charge of the electron, and V is the electric potential.
To find the electric potential at the midpoint, we need to calculate the electric potential due to each of the charges separately and then add them together.
The electric potential due to a point charge can be calculated using the equation:
V = k * q / r, where k is the Coulomb's constant, q is the charge of the point charge, and r is the distance from the point charge.
First, let's calculate the electric potential due to the +5.00 µC charge. Given that the distance from the midpoint to this charge is 14.0 cm = 0.14 m, we can use the equation:
V1 = (9 x 10^9 N m^2/C^2) * (5.00 x 10^-6 C) / 0.14 m
V1 = (9 x 10^9 * 5.00 x 10^-6) / 0.14
V1 = 3.214 x 10^5 V
Next, let's calculate the electric potential due to the +2.00 µC charge. Given that the distance from the midpoint to this charge is 46.0 cm = 0.46 m, we can use the equation:
V2 = (9 x 10^9 N m^2/C^2) * (2.00 x 10^-6 C) / 0.46 m
V2 = (9 x 10^9 * 2.00 x 10^-6) / 0.46
V2 = 3.913 x 10^5 V
Now, we can find the total electric potential at the midpoint by adding V1 and V2:
V_total = V1 + V2
V_total = 3.214 x 10^5 V + 3.913 x 10^5 V
V_total = 7.127 x 10^5 V
Finally, we can find the electric potential energy of the electron at the midpoint by multiplying the charge of the electron (which is -1.60 x 10^-19 C) with the total electric potential:
PE = (-1.60 x 10^-19 C) * (7.127 x 10^5 V)
PE = -1.141 x 10^-13 J
Therefore, the electric potential energy of the electron when it is at the midpoint, 14.0 cm from the 5.00 µC charge, is -1.141 x 10^-13 J.