The magnetic field in a travelling electromagnetic wave has a peak value of 20 nT. The peak value of electric field strength is : (1) 6 V/m (2) 9 V/m (3) 12 V/m (4) 3 V/m

To find the peak value of the electric field strength in a traveling electromagnetic wave when given the peak value of the magnetic field, we can use the relationship between the electric field (E) and the magnetic field (B) in electromagnetic waves. This relationship is defined by the equation:

Understanding the Relationship

In free space, the electric field and magnetic field are related by the equation:

E = cB

where:

• E is the peak electric field strength in volts per meter (V/m),
• B is the peak magnetic field strength in teslas (T), and
• c is the speed of light in a vacuum, approximately 3 x 10^8 m/s.

Converting Units

Before we can use this equation, we need to ensure that the magnetic field strength is in the correct units. The given peak magnetic field strength is:

B = 20 nT = 20 x 10^-9 T

Calculating the Electric Field Strength

Now we can substitute the values into the equation:

E = cB = (3 x 10^8 m/s)(20 x 10^-9 T)

Calculating this gives:

E = 3 x 10^8 x 20 x 10^-9 = 6 V/m

Final Result

Thus, the peak value of the electric field strength is 6 V/m. Therefore, the correct answer is option (1) 6 V/m.

Why This Matters

This relationship between electric and magnetic fields is fundamental in understanding how electromagnetic waves propagate through space. It shows that changes in one field can induce changes in the other, which is a key principle behind many technologies, including radio waves, microwaves, and even visible light.