An alpha particle (charge +2e and mass 6.64 x10-27 kg) is traveling to the right at 1.50 km/s. What uniform electric field (magnitude and direction) is needed to cause it to travel to the left at the same speed after 2.65 s.?
To answer the questions
An alpha particle (charge + 2e and mass 6.64 x 10-27 kg) is traveling to the right at 1.50km/s. What u niform electric field (magnitude and direction) is nee ded to cause it to travel to the left at the same speed af ter 2.65µs?
To determine the required electric field magnitude and direction to cause the alpha particle to travel in the opposite direction at the same speed after a given time, we can use the following steps:
1. Calculate the initial momentum of the alpha particle:
The momentum (p) of an object is given by the product of its mass (m) and velocity (v). In this case, the mass of the alpha particle is 6.64 x 10^-27 kg, and the initial velocity is 1.50 km/s (which can be converted to m/s by multiplying by 1000):
Initial momentum (p_initial) = mass (m) x initial velocity (v_initial)
2. Determine the time interval:
In this case, the given time interval is 2.65 seconds.
3. Calculate the change in momentum:
The change in momentum (Δp) can be calculated by subtracting the initial momentum from the final momentum. Since we want the alpha particle to travel at the same speed in the opposite direction, the final momentum (p_final) would be the negative value of the initial momentum:
Δp = p_final - p_initial
4. Calculate the acceleration:
Using the formula for acceleration (a) and the change in momentum (Δp), we can find the acceleration acting on the alpha particle during the time interval:
Acceleration (a) = Δp / time (t)
5. Calculate the electric field magnitude:
The electric field (E) exerted on a charged particle is related to the acceleration (a) by the formula:
E = a / charge (q)
Given that the alpha particle has a charge of +2e, where e is the elementary charge (1.6 x 10^-19 C), we can substitute the values into the equation to find the electric field magnitude.
6. Determine the direction of the electric field:
The direction of the electric field will be opposite to the desired direction of the alpha particle's motion. In this case, since we want the alpha particle to travel to the left, the electric field should be directed to the right.
By following these steps and applying the necessary calculations, you should be able to determine the required electric field magnitude and direction to cause the alpha particle to travel to the left at the same speed after 2.65 s.
acceleration= change in speed/time
= 3.0km/s
force= ma
also, force= Eq
E= ma/q