Question

In the microscopic view of electrical conduction in a copper wire, electrons are accelerated by an electric field and then collide with metal atoms after traveling about 3.4×10−8m. If an electron begins from rest and is accelerated by a field of 0.070 N/C, what is its speed when it collides with a metal atom?

Answer 1

Answer:

       $\large\boxed{\large\boxed{29m/s}}$

Explanation:

1. Obtain the net force acting on the electron

The electric force equals the magnetic field times the charge of the particle:

• $F=E\times q$

The charge on the electron is $1.602\times 10^{-19}C$.

• $F=0.070N/C\times 1.602\times 10^{-19}C=1.1214\times 10^{-20}N$

2. Calculate the acceleration of the electron

• Mass of an electron: 9.109 × 10⁻³¹ kg

       $F=m\times a\implies a=F/m\\\\ a=1.1214\cdot 10^{-20}N/(9.109\cdot 10^{-31}kg)=1.231\cdot 10^{10}m/s^2$

3. Calculate the speed

Uniformly accelerated motion:

                 $s^2=u^2+2ad\\ \\ s^2=0^2+2\times1.231\cdot 10^{10}m/s^2\times 3.4\cdot 10^{-8}m\\ \\ s^2=8.371\cdot 10^2m^2/s^2\\ \\ s=28.9m/s\approx 29m/s$