an electron is sitting 10cm away from a small object -5nc it is let go and moves away from the charged object when it reaches a distance of 15 cm away find its speed
To find the speed of the electron when it is 15 cm away from the charged object, we can use the concepts of electrical potential energy and conservation of energy.
First, let's determine the initial potential energy of the electron when it is 10 cm away from the charged object. The potential energy (U) of a charged object is given by the formula:
U = k * (q1 * q2) / r
Where:
k is the electrostatic constant (k ≈ 8.99 * 10^9 Nm^2/C^2)
q1 and q2 are the charges of the two objects (in this case, the charge of the electron (q1) is -1.6 * 10^-19 C, and the charge of the object (q2) is -5 * 10^-9 C)
r is the distance between the two objects (10 cm or 0.10 m in this case)
Substituting these values into the formula, we can find the initial potential energy:
U_initial = k * (q1 * q2) / r
= (8.99 * 10^9 Nm^2/C^2) * (-1.6 * 10^-19 C) * (-5 * 10^-9 C) / 0.10 m
Next, when the electron moves to a distance of 15 cm (or 0.15 m) away from the charged object, the potential energy becomes:
U_final = k * (q1 * q2) / r
= (8.99 * 10^9 Nm^2/C^2) * (-1.6 * 10^-19 C) * (-5 * 10^-9 C) / 0.15 m
Now, by applying the conservation of energy principle, the initial potential energy of the electron is equal to its final kinetic energy. The kinetic energy (K) of an object is given by the formula:
K = (1/2) * m * v^2
Where:
m is the mass of the electron (m ≈ 9.11 * 10^-31 kg)
v is the velocity or speed of the electron (what we want to find)
Setting the initial potential energy equal to the final kinetic energy, we can solve for the speed of the electron:
U_initial = K_final
=> (1/2) * m * v^2 = U_final
Solving for v:
v^2 = (2 * U_final) / m
v = sqrt((2 * U_final) / m)
Now, substituting the values of U_final and m into the equation, we can find the speed of the electron when it is 15 cm away from the charged object.