Find the lengths of each of the following vectors

Answer:

The final size is nearly the same as the initial size because the increase in size is remarkably small

Solution:

According to the problem:

The proton beam energy is E = 250 GeV =

Distance traveled by the photon, d = 1 km = 1000 m

Proton mass,

Initial size of the wave packet,

Now,

This operates under relativistic principles

The rest mass energy for the proton is expressed as:

This proton energy is

Thus, the speed of the proton, v

The time to cover 1 km = 1000 m of distance is calculated as:

T =

T =

According to the dispersion factor;

Thus, the widening of the wave packet is relatively minor.

Hence, we can conclude that:

where

= final width

Answer:

The potential energy tied to the charge diminishes.

The electric field performs negative work on the charge.

Explanation:

For this issue, the answer is clarified as the system takes in energy (+). The surroundings contribute 84 KJ of work. Whenever a system is receiving work from its surroundings, the value will be positive. Therefore, it sums to 12.4 KJ + 4.2 = 16.6 KJ.