An electron moving parallel to the x axis has an initial speed of 3.66 ✕ 106 m/s at the origin. Its speed is reduced to 1.40 ✕ 105 m/s at the point x = 2.00 cm. Calculate the potential difference between the origin and that point.

ΔV =

1.68

To calculate the potential difference between the origin and the point x = 2.00 cm, we can use the formula:

ΔV = V2 - V1

where ΔV is the potential difference, V2 is the potential at point x = 2.00 cm, and V1 is the potential at the origin.

In order to proceed, we need to find the potential at each point. The electric potential (V) is given by the formula:

V = (1/4πε₀) * (q/r)

where ε₀ is the permittivity of free space, q is the charge, and r is the distance from the charge.

Since we are dealing with an electron, the charge (q) is -1.6 × 10^-19 C. The distance (r) from the origin to point x = 2.00 cm is 0.02 m.

Let's calculate V2:

V2 = (1/4πε₀) * (q/r) = (1/4πε₀) * (-1.6 × 10^-19 C / 0.02 m)

Now, let's calculate V1:

V1 = (1/4πε₀) * (q/r) = (1/4πε₀) * (-1.6 × 10^-19 C / 0 m)

Note that the potential at the origin is zero since there is no charge there.

Finally, we can substitute the values of V2 and V1 into the formula for potential difference:

ΔV = V2 - V1

Solving this equation will give us the desired potential difference.