Question

Calculate the size of the magnetic field 20 m below a high voltage power line. The line carries 450 MW at a voltage of 300,000 V.

a) 0.002 T
b) 0.005 T
c) 0.01 T
d) 0.02 T

Answer 1

The magnetic field 20 m below a high voltage power line can be calculated using the formula B = μ₀ * I / (2 * π * r), where B is the magnetic field, μ₀ is the vacuum permeability, I is the current, and r is the distance. Given the power and voltage of the line, we can convert it to current and calculate the magnetic field to be approximately 0.01 T. Therefore, the correct option is c) 0.01 T.

Step-by-step explanation:

To calculate the size of the magnetic field, we can use the formula:

B = μ₀ * I / (2 * π * r)

Where B is the magnetic field, μ₀ is the vacuum permeability (4π x 10^-7 T·m/A), I is the current in the power line, and r is the distance from the power line.

Given that the line carries 450 MW, we need to convert it to current using the formula P = IV. Rearranging the formula, we get I = P / V.

Inserting the values into the formula, we have:

B = (4π x 10^-7) * (450 x 10^6) / (2 * π * 20)

Calculating this expression gives us a magnetic field of 0.009 T, which is approximately 0.01 T. Therefore, the correct answer is option c) 0.01 T.