Chapter 17, Problem 4Q

An electron is accelerated from rest by a potential difference of 0.20 V. How much greater would its final speed be if it is accelerated with four times as much voltage? Explain.

To determine

How much greater would an electron’s final speed will be if it is accelerated with four times as much voltage.

Answer to Problem 4Q

Solution:

Speed will be 2 times.

Explanation of Solution

Potential difference between two points, ${\text{V}}_{ba}=V_b-V_a=\frac{P{E}_b-P{E}_a}{q}$, where $PE$ is the potential energy and q is the charge.

Kinetic energy, $K.E=\frac{1}{2}m{v}^2$, where m is the mass and v is the velocity

Formula used:

Calculation:

We have ${\text{V}}_{ba}=V_b-V_a=\frac{P{E}_b-P{E}_a}{q}$

When potential increases to four times potential energy also increases by four times

We know when charge moves potential energy is converted to kinetic energy, so when potential energy increases to four times kinetic energy also increases to four times.

We have Kinetic energy, $K.E=\frac{1}{2}m{v}^2$

So, when kinetic energy increases to four times speed increases by 2 times.