Two electrons are fiXed 2 cm apart .another eleCtron is shot from infinity and stops midway between the two .what is the initial speed?
To find the initial speed of the third electron, we need to use the principle of conservation of energy.
The total energy of the third electron can be calculated as the sum of its kinetic energy and its electrical potential energy. Initially, the electron is at infinity, so its kinetic energy is zero.
The electrical potential energy is given by the equation:
PE = k * (q1 * q2) / r
where k is the Coulomb's constant (k ≈ 9 × 10^9 N m^2/C^2), q1 and q2 are the charges of the two fixed electrons (which are both equal to the charge of an electron, -1.6 × 10^-19 C), and r is the distance between the third electron and each of the fixed electrons (2 cm = 0.02 m).
Since the third electron stops midway between the two fixed electrons, the electrical potential energy is equal to its initial kinetic energy when it stops. So we can write:
0.5 * m * v^2 = k * (q1 * q2) / r
where m is the mass of the electron (9.1 × 10^-31 kg) and v is its initial speed that we want to find.
We can rearrange the equation to solve for v:
v = √(2 * k * (q1 * q2) / (m * r))
Substituting the known values, we get:
v = √(2 * 9 × 10^9 N m^2/C^2 * (-1.6 × 10^-19 C)^2 / (9.1 × 10^-31 kg * 0.02 m))
After evaluating this expression, the initial speed of the third electron is approximately 4.83 × 10^6 m/s.