Question

What is the force per meter on a lightning bolt at the equator that carries 20,000 A perpendicular to the Earth's 3.00×10^-5-T field?

a) 2.4 × 10-2 N/m
b) 6.0 × 10-2 N/m
c) 1.8 × 10-1 N/m
d) 4.5 x 10-1 N/m

Answer 1

The force per meter on a lightning bolt at the equator carrying 20,000 A perpendicular to the Earth's 3.00 × 10^-5-T field is 0.6 N. The force will act toward the east, as dictated by the right-hand rule.

Step-by-step explanation:

Calculating Force on a Lightning Bolt at the Equator

To calculate the force per meter on a lightning bolt that carries a current of 20,000 A perpendicular to the Earth's magnetic field at the equator, we use the formula for the magnetic force on a current-carrying conductor: F = I * L * B * sin(θ), where:

• I is the current in amperes (A)
• L is the length of the conductor in meters (m) - here, we'll consider it per meter
• B is the magnetic field strength in teslas (T)
• θ is the angle between the current and the magnetic field, which is 90 degrees since the current is perpendicular to the field

Since sin(90°) = 1, the formula simplifies to F = I * B. When we insert the given values:

F = 20,000 A * 3.00 × 10^-5 T = 0.6 N

The direction of the force is determined by the right-hand rule. With the current going straight up (out of the palm) and the Earth's magnetic field going to the right (direction of the fingers), the force will act outwards — perpendicular to both the current and the magnetic field (direction of the thumb), which in this case is due east.