Question

The electric field \(\vec{E}\) of an electromagnetic wave propagating in north direction is oscillating in up and down direction. Describe the direction of magnetic field \(\vec{B}\) of the wave.
(b) Are the wave length of radio waves and microwaves longer or shorter than those detectable by human eyes ?
(c) Write main use of each of the following in human life :
(i) Infrared waves (ii) Gamma rays

Hint:

E, B and the direction of travel are mutually perpendicular, so B is along east-west. Radio waves and microwaves are longer than visible light. Infrared is used for heating or remote controls, gamma rays for cancer therapy.

Answer 1

Step 1: Direction of B (part a):
In an electromagnetic wave \(\vec{E}\), \(\vec{B}\) and the direction of travel are mutually perpendicular. The wave travels along \(\vec{E} \times \vec{B}\).
Take north as \(+\hat{j}\) and up as \(+\hat{k}\). Then \(\vec{E}\) is along \(\pm\hat{k}\) and the wave goes along \(+\hat{j}\).
We need \(\hat{k} \times \vec{B}\) to point along \(\hat{j}\). Since \(\hat{k} \times \hat{i} = \hat{j}\), the field \(\vec{B}\) must be along \(+\hat{i}\) (east) when E points up.
When E points down, B points west. So \(\vec{B}\) oscillates along the east-west line, in phase with E.

Step 2: Wavelengths (part b):
Human eyes detect visible light, with wavelength from about 400 nm to 700 nm.
Radio waves have wavelengths from about 0.1 m to several kilometres. Microwaves have wavelengths from about 1 mm to 0.1 m.
Both are far above 700 nm. So the wavelengths of radio waves and microwaves are longer than those of visible light.

Step 3: Uses (part c):
(i) Infrared waves are called heat waves. They are used in physiotherapy, in TV and AC remote controls, in night-vision cameras and for warming greenhouses.
(ii) Gamma rays have the highest energy. They are used in radiotherapy to destroy cancer cells and to sterilise medical equipment and food.

Final Answer:
(a) B oscillates along the east-west direction. (b) Longer. (c) (i) Infrared waves: heating, physiotherapy, remote controls. (ii) Gamma rays: treatment of cancer.