Question

S18-MP4 roblem 26.23 K) 8 of 10 How far does the proton travel before reaching its turning point? Express your answer with the appropriate units. View Available Hint(s) Constants | Periodic Table on an infinite charged plane is -1.60x10-6 C/m2 . A proton is shot straight away from the plane at 2.30x106 m/s Hint 1. How to approach this problem When the proton has reached its farthest point, it is standing still. This means that the work done on the proton by the electric field of the infinite sheet has exactly canceled the original kinetic energy of the proton. Hint 2. What is the work done by the sheet Recall that the electric field near an infinite sheet of charge density ? is given by E Since the electric field strength is independent of the distance from the sheet, the force is constant along the path of the proton and the work done is simply equal to the force times the distance traveled. Value Units Submit

Answer 1

The electric field strength near an infinite sheet of charge density σ is given by E = σ/2ε0, where ε0 is the electric constant.

The force on the proton due to the electric field of the sheet is F = qE, where q is the charge of the proton.

The work done by the sheet on the proton is W = Fd, where d is the distance traveled by the proton before reaching its turning point.

When the proton has reached its turning point, its kinetic energy is zero, so the work done by the electric field of the sheet must equal the initial kinetic energy of the proton, which is given by KE = (1/2)mv^2, where m is the mass of the proton and v is its initial velocity.

Setting these two expressions for work equal to each other, we have:

F d = (1/2)mv^2

Substituting F = qE and E = σ/2ε0, we get:

qd/2ε0 = (1/2)mv^2

Solving for d, we get:

d = mv^2/(qσε0)

Substituting the given values for m, v, q, and σ, and the value of ε0 from the constants, we get:

d = (1.67x10^-27 kg)(2.30x10^6 m/s)^2/(1.60x10^-6 C/m^2)(2ε0) ≈ 1.59x10^-5 m

Therefore, the proton travels a distance of approximately 1.59x10^-5 meters before reaching its turning point.