A proton is released 2*10^-11 from the center of an immovable 6.4*10^-18 C charged sphere. What is the speed of this proton when it is 0.50mm from the center of the sphere?
Kinetic energy = (1/2) m v^2
Change of potential energy = kinetic energy.
Do the other problem the same way.
To find the speed of the proton when it is 0.50 mm from the center of the charged sphere, we can use the principle of conservation of energy. The proton has an initial potential energy due to its distance from the charged sphere, and as it moves closer, this potential energy is converted into kinetic energy.
First, let's find the initial potential energy of the proton when it is 2*10^-11 m from the center of the sphere. The potential energy (U) is given by the equation:
U = k * (q1 * q2) / r
where k is the electrostatic constant (9 * 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Plugging in the values, we have:
U = (9 * 10^9 Nm^2/C^2) * (6.4 * 10^-18 C) * (1.6 * 10^-19 C) / (2 * 10^-11 m)
U = (9 * 6.4 * 1.6) * (10^-9 * 10^-18 * 10^-19 * 10^11) J
U = (92.16) * (10^-9 * 10^-18 * 10^-19 * 10^11) J
U = 92.16 * 10^-35 J
Now, let's find the initial kinetic energy of the proton when it reaches a distance of 0.50 mm (or 0.50 * 10^-3 m) from the center of the sphere. The kinetic energy (K) is given by the equation:
K = (1/2) * m * v^2
where m is the mass of the proton and v is its velocity.
To find the mass of the proton, we can use its known value, which is approximately 1.67 * 10^-27 kg.
Plugging in the values, we have:
K = (1/2) * (1.67 * 10^-27 kg) * v^2
Now, using the principle of conservation of energy, we know that the total initial energy (U) is equal to the total final energy (K). Therefore:
U = K
92.16 * 10^-35 J = (1/2) * (1.67 * 10^-27 kg) * v^2
Simplifying the equation:
v^2 = (2 * 92.16 * 10^-35 J) / (1.67 * 10^-27 kg)
v^2 = (2 * 92.16) * (10^-35 J / 10^-27 kg)
v^2 = (2 * 92.16) * 10^-8 m^2/s^2
v^2 = 184.32 * 10^-8 m^2/s^2
v^2 = 1.8432 * 10^-6 m^2/s^2
v = sqrt(1.8432 * 10^-6) m/s
v ≈ 0.00136 m/s
Therefore, the speed of the proton when it is 0.50 mm from the center of the sphere is approximately 0.00136 m/s.