A proton is moving parallel to a uniform electric field. The electric field accelerates the proton and increases its linear momentum to 5.0 10-23 kg m/s from 1.4 10-23 kg m/s in a time of 6.5 10-6 s. What is the magnitude of the electric field?
To find the magnitude of the electric field, we can use the equation for the change in linear momentum, which is given by:
Δp = m * Δv
Where:
Δp = change in linear momentum
m = mass of the proton
Δv = change in velocity
First, let's find the change in velocity Δv:
Δv = final velocity - initial velocity
Δv = (5.0 * 10^-23) kg m/s - (1.4 * 10^-23) kg m/s
Δv = 3.6 * 10^-23 kg m/s
Now, we need to find the acceleration of the proton. The acceleration is given by:
a = Δv / t
Where:
a = acceleration
t = time
Plugging in the values:
a = (3.6 * 10^-23) kg m/s / (6.5 * 10^-6) s
a ≈ 5.538 * 10^-17 m/s^2
Since the proton is moving parallel to the uniform electric field, the force on the proton is given by:
F = q * E
Where:
F = force
q = charge of the proton
E = electric field
The force can also be expressed as the product of mass and acceleration:
F = m * a
Equating the two equations and solving for the electric field E:
m * a = q * E
E = (m * a) / q
The charge of a proton is q = 1.6 * 10^-19 C, and the mass of a proton is m = 1.67 * 10^-27 kg. Plugging in the values:
E = (1.67 * 10^-27 kg * 5.538 * 10^-17 m/s^2) / (1.6 * 10^-19 C)
E ≈ 5.448 * 10^11 N/C
Therefore, the magnitude of the electric field is approximately 5.448 * 10^11 N/C.
To find the magnitude of the electric field, we can use the equation:
Δp = q * E * Δt
Where:
Δp = change in linear momentum (final momentum - initial momentum)
q = charge of the particle (charge of a proton = +1.6 x 10^-19 C)
E = magnitude of the electric field
Δt = change in time (final time - initial time)
Given:
Initial momentum (p1) = 1.4 x 10^-23 kg m/s
Final momentum (p2) = 5.0 x 10^-23 kg m/s
Δt = 6.5 x 10^-6 s
First, let's calculate the change in momentum:
Δp = p2 - p1
Δp = (5.0 x 10^-23 kg m/s) - (1.4 x 10^-23 kg m/s)
Δp = 3.6 x 10^-23 kg m/s
Now, we can plug in the values into the equation to find the magnitude of the electric field:
Δp = q * E * Δt
3.6 x 10^-23 kg m/s = (1.6 x 10^-19 C) * E * (6.5 x 10^-6 s)
Simplifying the equation:
E = (3.6 x 10^-23 kg m/s) / [(1.6 x 10^-19 C) * (6.5 x 10^-6 s)]
E ≈ 1.126 x 10^6 N/C
Therefore, the magnitude of the electric field is approximately 1.126 x 10^6 N/C.
Impulse = change in momentum
coulomb force*time=changemomentum
Eq*time= changemomentum
solve for E