Question

Consider a long, closely wound solenoid with 10,000 turns per meter. A What current, in amperes, is needed in the solenoid to produce a magnetic field inside the solenoid, near its center, that is 10⁴

times the Earth's magnetic field of 5.1×10−⁵T ?

Answer 1

To find the current needed to create a magnetic field 10,000 times the Earth's magnetic field in a solenoid with 10,000 turns per meter, one must multiply the Earth's field by 10,000, then divide by the product of the permeability of free space and the number of turns per meter.

Step-by-step explanation:

The student is asking for the current needed in a solenoid to produce a magnetic field that is 10,000 times the Earth's magnetic field. The Earth's magnetic field is given as 5.1×10⁻⁵ T and the solenoid has 10,000 turns per meter. To calculate this, we use the solenoid magnetic field formula B = μ0 * n * I where B is the magnetic field, μ0 is the permeability of free space (μ0 = 4π×10⁻⁷ T·m/A), n is the number of turns per meter, and I is the current in amperes.

To get the desired magnetic field strength, which is 10,000 times the Earth's magnetic field, we need to use the following calculation:

1. Multiply the Earth's magnetic field by 10,000 to get the target magnetic field within the solenoid: Btarget = 10,000 * 5.1×10⁻⁵ T.
2. Rearrange the formula to solve for I: I = Btarget / (μ0 * n).
3. Substitute the known values and calculate the current I.

It is important to note that the permeability of free space is a constant and the number of turns per meter of the solenoid is given. Using these values allows us to solve for the current needed to achieve the target magnetic field strength.