Question

An 8.0-m-diameter, 25-m-long cylindrical spaceship needs to have an internal magnetic field with the same strength as earth's. A clever astronaut suggests wrapping the spaceship tightly with 1.1-mm -diameter wire, then using the spaceship's antimatter generator to drive a current through the coil. How much current will be needed?

Answer 1

To calculate the needed current to create a magnetic field equivalent to Earth's inside a cylindrical spaceship wrapped with wire, we use the solenoid formula and consider the total number of turns and the permeability of free space.

Step-by-step explanation:

The question involves calculating the current needed in a wire wrapped around a cylindrical spaceship to create a magnetic field equivalent to Earth's. To solve this problem, we need to use the formula for the magnetic field inside a solenoid (B = μ0 * n * I), where B is the magnetic field strength, μ0 is the permeability of free space (4π x 10-7 Tm/A), n is the number of turns per meter, and I is the current. Since the spaceship acts as a solenoid when wrapped with wire, we can find the number of turns per meter by dividing the total number of turns by the length of the spaceship. Given the diameter of the wire and the diameter of the spaceship, we can calculate the number of turns by finding the circumference of the spaceship and dividing it by the diameter of the wire. Then, knowing the Earth's magnetic field strength and the number of turns per meter, we apply the formula to find the required current, I.

Answer 2

the current needed to produce an internal magnetic field with the same strength as Earth's is approximately 2.27 million Amperes.

Step-by-step explanation:

An 8.0-m-diameter, 25-m-long cylindrical spaceship needs to have an internal magnetic field with the same strength as earth's. A clever astronaut suggests wrapping the spaceship tightly with 1.1-mm -diameter wire, then using the spaceship's antimatter generator to drive a current through the coil. How much current will be needed?

To determine the amount of current needed to produce an internal magnetic field of the same strength as Earth's, we can use Ampere's law. Ampere's law relates the magnetic field produced by a current-carrying wire to the current flowing through it.

The equation for Ampere's law is:

B = μ₀ * (I / 2πr)

Where:

B is the magnetic field produced by the wire

μ₀ is the permeability of free space (constant value of 4π x 10^-7 T·m/A)

I is the current flowing through the wire

r is the radius of the wire

In this case, the radius of the wire is given as 1.1 mm, which is 0.0011 m. The desired magnetic field strength is the same as Earth's, which is approximately 25 to 65 microteslas (µT).

Let's calculate the current needed for the spaceship:

B = 25 x 10^-6 T (Considering the lower end of Earth's magnetic field strength)

r = 0.0011 m

μ₀ = 4π x 10^-7 T·m/A

Plugging these values into the equation, we can solve for I:

25 x 10^-6 T = (4π x 10^-7 T·m/A) * (I / 2π * 0.0011 m)

Simplifying the equation:

25 x 10^-6 T = (4π x 10^-7 T·m/A) * (I / 2π * 0.0011 m)

25 = 10^-7 * I / 0.0011

I = 0.025 / 10^-7 * 0.0011

I ≈ 2.27 x 10^6 A

Therefore, the current needed to produce an internal magnetic field with the same strength as Earth's is approximately 2.27 million Amperes.