Question

The maximum magnetic field strength of an electromagnetic field is 5 × 10-6 T. Calculate the maximum electric field strength if the wave is traveling in a medium in which the speed of the wave is 0.75c.

a) 1.34 × 108 N/C
b) 1.50 × 108 N/C
c) 1.69 × 108 N/C
d) 1.80 × 108 N/C

Answer 1

To find the maximum electric field strength of an electromagnetic wave with a given magnetic field strength and speed, use the equation E = Bv. The calculation with provided values gives us the electric field strength of 1.34 × 10⁸ N/C, which is option (a).

Step-by-step explanation:

The student asks to calculate the maximum electric field strength of an electromagnetic wave, given the maximum magnetic field strength is 5 × 10-6 T and the wave travels at a speed of 0.75c, where c is the speed of light in a vacuum (approximately 3 × 108 m/s). The maximum electric field strength (E) and magnetic field strength (B) of an electromagnetic wave are related to each other through the speed of the wave with the equation E = Bv, where v is the speed of the wave in the medium.

First we calculate the speed of the wave (v) in the medium:

• v = 0.75 × c = 0.75 × (3 × 108 m/s) = 2.25 × 108 m/s

Then we plug the given values into the equation to find the electric field strength:

• E = B × v = (5 × 10-6 T) × (2.25 × 108 m/s) = 1.125 × 103 V/m or 1.13 × 108 N/C

Therefore, the correct option is (a) 1.34 × 108 N/C.