Question

A straight infinitely long cylinder of radius R₀ = 10 cm is uniformly charged with a surface charge density σ = + 10^-12 C/m². The cylinder serves as a source of electrons, with the velocity of the emitted electrons perpendicular to its surface. Electron velocity must be ______ × 10⁵ m/s to ensure that electrons can move away, from the axis of the cylinder to a distance greater than r = 10³ m.

Options

• 1.00

• 2.00

• 3.00

• 4.00

Answer 1

A straight infinitely long cylinder of radius R₀ = 10 cm is uniformly charged with a surface charge density σ = + 10^-12 C/m². The cylinder serves as a source of electrons, with the velocity of the emitted electrons perpendicular to its surface. Electron velocity must be 4.00 × 10⁵ m/s to ensure that electrons can move away, from the axis of the cylinder to a distance greater than r = 10³ m.

Explanation:

 

`1/2mv^2 = (lambdae)/(2pi∈_0) log n r/R_0`

`v = sqrt((lambdae)/(pi∈_0m)log  r/R_0)`

σ = `Q/(2piR_0 xx L)`

`lambda = Q/L = sigma xx 2piR_0`

∴ `v = sqrt((2sigmaeR_0)/(∈_0m) log  r/R_0)`

`3.7 xx 10^5` m/s

or  `4 xx 10^5` m/s