a) The Earth magnetic field on the equator is directed horizontally from South to North. A power line with the direct current (i.e. always in the same direction) of 100 A runs also horizontally from East to West. You measure the total magnetic field at 20 m directly below the power line. What will be the total magnetic field strength and direction? µ0=4π∗10−7T/
m/A.
To determine the total magnetic field strength and direction at the point directly below the power line, we need to consider the contributions of both the Earth's magnetic field and the current-carrying power line.
The magnetic field produced by a current-carrying wire is given by the Biot-Savart law, which states that the magnetic field strength at a distance r from a wire carrying current I is given by:
B = (µ0 * I) / (2πr)
Where:
B = magnetic field strength
µ0 = magnetic constant (4π * 10^-7 T*m/A)
I = current (100 A)
r = distance from the wire (20 m)
Plugging in the values:
B_line = (4π * 10^-7 * 100) / (2π * 20) = 2 * 10^-6 T
The direction of the magnetic field produced by the current-carrying wire would be perpendicular to the direction of the current flow, and using the right-hand rule (curled fingers point in the direction of the current, thumb points in the direction of the magnetic field), the field would be directed vertically upwards at the point directly below the wire.
The Earth's magnetic field at the equator is directed horizontally from South to North. The total magnetic field at the point below the power line would be the vector sum of the Earth's magnetic field and the magnetic field produced by the power line.
Since the Earth's magnetic field and the magnetic field produced by the power line are perpendicular to each other, we can find the total magnetic field strength using the Pythagorean theorem:
B_total = √((B_earth)^2 + (B_line)^2)
Plugging in the values:
B_total = √((0)^2 + (2 * 10^-6)^2) = 2 * 10^-6 T
The total magnetic field strength at the point directly below the power line is 2 * 10^-6 Tesla, and the direction is vertical upwards.