The magnitude of the electric field at the dot is : 10⁴ v/m
<h3>What is electric field?</h3>
Electric field is a region around a charged particle or object within which a force would be exerted on other charged particles or objects.
Given that there are three equipotential lines with equal spacing,we will apply the the relationship between P.D and electric field
Determine the magnitude of the electric field at the dot
change in voltage = E .d

From equation ( 1 )
The magnitude of electric field will be given as


Hence we can conclude that The magnitude of the electric field at the dot is : 10⁴ v/m
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Answer:
d = 2.54 [m]
Explanation:
Through the theorem of work and energy conservation, we can find the work that is done. Considering that the energy in the initial state is only kinetic energy, while the energy in the final state is also kinetic, however, this is zero since the body stops.

where:
W = work [J]
Ek1 = kinetic energy at initial state [J]
Ek2 = kinetic energy at the final state = 0.
We must remember that kinetic energy can be calculated by means of the following expression.
![\frac{1}{2} *m*v^{2}-W=0\\W= \frac{1}{2} *4*(5)^{2}\\W= 50 [J]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%2Am%2Av%5E%7B2%7D-W%3D0%5C%5CW%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A4%2A%285%29%5E%7B2%7D%5C%5CW%3D%2050%20%5BJ%5D)
We know that work is defined as the product of force by distance.

where:
F = force [N]
d = distance [m]
But the friction force is equal to the product of the normal force (body weight) by the coefficient of friction.
![f=m*g*0.5\\f = 4*9.81*0.5\\f = 19.62 [N]](https://tex.z-dn.net/?f=f%3Dm%2Ag%2A0.5%5C%5Cf%20%3D%204%2A9.81%2A0.5%5C%5Cf%20%3D%2019.62%20%5BN%5D)
Now solving the equation for the work.
![d=W/F\\d = 50/19.62\\d = 2.54[m]](https://tex.z-dn.net/?f=d%3DW%2FF%5C%5Cd%20%3D%2050%2F19.62%5C%5Cd%20%3D%202.54%5Bm%5D)
The magnetic force experienced by the proton is given by

where q is the proton charge, v its velocity, B the magnitude of the magnetic field and

the angle between the direction of v and B. Since the proton moves perpendicularly to the magnetic field, this angle is 90 degrees, so

and we can ignore it in the formula.
For Netwon's second law, the force is also equal to the proton mass times its acceleration:

So we have

from which we can find the magnitude of the field:
Answer:
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