Chapter 16, Problem 41P

(a)

To determine

The speed of the electron.

Answer to Problem 41P

The speed of the electron is $7.48\times {10}^6\text{m/s}$ .

Explanation of Solution

Given info:

The mass of the electron is $m=9.11\times {10}^{-31}\text{kg}$ .

The charge on electron is $q=1.6\times {10}^{-19}\text{C}$ .

The electric field is $E=1.45\times {10}^4\text{N/C}$ .

The separation of the plates is $d=1.10\text{cm}$ .

Formula used:

According to the law of conservation of energy,

  $\begin{array}{c}Eqd=\frac{1}{2}m{v}^2\\ v=\sqrt{\frac{2Eqd}{m}}\end{array}$

Calculation:

Substituting the given values, we get

  $\begin{array}{c}v=\sqrt{\frac{2\left(1.45\times {10}^4\text{N/C}\right)\left(1.6\times {10}^{-19}\text{C}\right)\left(1.1\times {10}^{-2}\text{m}\right)}{9.11\times {10}^{-31}\text{kg}}}\\ =7.48\times {10}^6\text{m/s}\end{array}$

Conclusion:

Thus, the speed of the electron is $7.48\times {10}^6\text{m/s}$ .

(b)

To determine

The proof to show that the gravitational force can be ignored.

Answer to Problem 41P

It is shown that gravitational force can be ignored.

Explanation of Solution

Given info:

The mass of the electron is $m=9.11\times {10}^{-31}\text{kg}$ .

The charge on electron is $q=1.6\times {10}^{-19}\text{C}$ .

The electric field is $E=1.45\times {10}^4\text{N/C}$ .

The separation of the plates is $d=1.10\text{cm}$ .

Formula used:

The gravitational force is given by,

  $F_g=mg$

The electric force is given by,

  $F_e=Eq$

Calculation:

Substituting the given values in formula $F_g=mg$ , we get

  $\begin{array}{c}{F}_g=\left(9.11\times {10}^{-31}\text{kg}\right)\left(9.8{\text{m/s}}^{\text{2}}\right)\\ =8.92\times {10}^{-30}\text{N}\end{array}$

Substituting the given values in formula $F_e=Eq$ , we get

  $\begin{array}{c}{F}_e=\left(1.45\times {10}^4\text{N/C}\right)\left(1.6\times {10}^{-19}\text{C}\right)\\ =2.32\times {10}^{-15}\text{C}\end{array}$

Compared to the electric force, the gravitational force is far less.

Conclusion:

Thus, the gravitational force can be ignored.