Question

In a microwave oven, electrons describe circular motion in a magnetic field within a special tube called amagnetron; as you'll learn in Chapter 29, the electrons' motion results in the production of micowaves. The electrons circle at a frequency of 2.15 GHz . The magnetron can accommodate electron orbits with maximum diameter 2.62 mm .
Part A

What's the magnetic field strength?

Part B

What's the electrons' energy in eV.

Answer 1

Answer:

The magnetic field strength and the electrons' energy are 0.077 T and 0.8906 eV.

Explanation:

Given that,

Diameter = 2.62 mm

Frequency = 2.15 GHz

(A). We need to calculate the magnetic field strength

Using formula of the magnetic field strength

$B=\dfrac{2\pi mf}{e}$

Where, f = frequency

e = charge of electron

Put the value into the formula

$B=\dfrac{2\times3.14\times9.1\times10^{-31}\times2.15\times10^{9}}{1.6\times10^{-19}}$

$B=0.077\ T$

(B). We need to calculate the energy of electron

Using formula of energy

$E=\dfrac{1}{2}m(r\omega)^2$

$E=\dfrac{1}{2}\times9.1\times10^{-31}\times(1.31\times10^{-3}\times2\pi\times2.15\times10^{9})^2$

$E=1.4249\times10^{-16}\ J$

The energy in eV

$1 eV=1.6\times10^{-16}\ J$

$E=\dfrac{1.4249\times10^{-16}}{1.6\times10^{-16}}$

$E=0.8906\ eV$

Hence, The magnetic field strength and the electrons' energy are 0.077 T and 0.8906 eV.