Question

Calculate the initial (from rest) acceleration of a proton in a 5.00×10⁶ N/C electric field (such as created by a research Van de Graaff). Explicitly show how you follow the steps in the ProblemSolving Strategy for electrostatics.

a) ( 8.60 X 10¹2 m/s² )
b) ( 3.80 X 10⁶ m/s² )
c) ( 8.60 X 10⁶ m/s² )
d) ( 3.80 X 10¹2 m/s² )

Answer 1

inal answer:

Using Newton's second law and the force on a charge in an electric field, the initial acceleration of a proton in a 5.00 × 10⁶ N/C electric field is calculated to be 4.79 × 10ⁱ⁴ m/s² by dividing the electric force acting on the proton by its mass.

Step-by-step explanation:

To calculate the initial acceleration of a proton in a 5.00 × 10⁶ N/C electric field, we will use Newton's second law and the formula for the force on a charge in an electric field. The force on the proton is given by F = qE, where q is the charge of the proton (1.60 × 10⁻¹¹ C) and E is the electric field strength. Newton's second law states that F = ma, where m is the mass of the proton (1.67 × 10⁻²⁷ kg) and a is the acceleration we want to find.

Combining these equations, we have:

1. F = qE = (1.60 × 10⁻¹¹ C) × (5.00 × 10⁶ N/C)
2. F = 8.00 × 10⁻¹³ N (the force on the proton)
3. a = F/m = (8.00 × 10⁻¹³ N) / (1.67 × 10⁻²⁷ kg) = 4.79 × 10⁻¹´ kg (the acceleration of the proton)

We have used the known values of the proton's charge and mass, and the given electric field strength, to calculate the force and subsequently the acceleration. Therefore, the initial (from rest) acceleration of the proton is 4.79 × 10ⁱ⁴ m/s².