The proton's speed is determined by the electric field strength and the distance between the plates. Using the equation v = √(2E/m), we find that the proton's speed is approximately 1.42 × 10⁵ m/s.
Determine what is the proton's speed?
To find the proton's speed, we can use the equation of motion for uniform acceleration. In this case, the electric field between the plates of the capacitor provides a constant acceleration to the proton.
The electric field strength (E) is given as 4.90 × 10⁴ N/C, and the distance between the plates (d) is 2.30 mm, which is equivalent to 2.30 × 10⁻³ m.
We can use the equation: E = (1/2)mv², where E is the electric field strength, m is the mass of the proton, and v is its final velocity. The mass of a proton (m) is approximately 1.67 × 10⁻²⁷ kg.
Rearranging the equation to solve for v, we get v = √(2E/m).
Plugging in the values, v = √(2 × 4.90 × 10⁴ N/C × 2.30 × 10⁻³ m / 1.67 × 10⁻²⁷ kg), and solving this expression gives v ≈ 1.42 × 10⁵ m/s as the proton's speed when it reaches the negative plate.
Therefore, the proton's speed when it reaches the negative plate is approximately 1.42 × 10⁵ m/s.
Complete question here:
The electric field strength is 4.90×104 N/C inside a parallel-plate capacitor with a 2.30 mm spacing. A proton is released from rest at the positive plate.
What is the proton's speed when it reaches the negative plate?