To determine the time interval over which the proton comes to rest, we can use the principle of work-energy.
First, we need to calculate the work done on the proton. The work done by the electric field is given by the equation:
W = q * ΔV
where W is the work done, q is the charge of the proton, and ΔV is the change in electric potential. In this case, since the proton comes to rest, the change in electric potential is equal to the initial electric potential.
Therefore, ΔV = -E * Δx
where E is the electric field and Δx is the distance travelled by the proton. Plugging in the values:
ΔV = -(-6x10^5 N/C) * 0.07m = 4.2x10^4 J
Since the work done on the proton is equal to the change in its kinetic energy, we can write:
ΔK = W
Solving for the change in kinetic energy:
ΔK = (1/2) * m * (v^2 - 0^2)
Since the proton comes to rest, the final velocity (v) is zero. Therefore:
ΔK = (1/2) * m * (0 - 0^2)
ΔK = 0
Setting the work done on the proton equal to zero:
0 = 4.2x10^4 J
This tells us that zero work was done on the proton, which means it lost all its initial kinetic energy and converted it into electric potential energy.
Now, let's calculate the initial kinetic energy of the proton:
K = (1/2) * m * v^2
Since it is given that the initial velocity and initial kinetic energy are both zero, we can write:
0 = (1/2) * m * (0^2)
0 = 0, which is true.
Therefore, the time interval over which the proton comes to rest is instantaneous, as it loses all its initial kinetic energy and comes to rest immediately.
At1=0, a proton is projected in the positive x-direction into a region of a uniform electric field of E=-6x1051. The proton travels 7.00 cm as it comes to rest. Determine The time interval over which the proton comes to rest
in simple steps
1 answer