Final answer:
To calculate the conventional current in a wire needed to produce a magnetic field twice that of the Earth's at a 5.0 cm distance, we use Ampère's Law and rearrange the formula B = (u0*I)/(2*π*r) to solve for the current. After plugging in the magnetic field strength of four times 10⁻⁵ T (two times the Earth's field) and the distance of 5.0 cm, we can calculate the required current.
Step-by-step explanation:
The student is asking how to calculate the conventional current flowing in a wire that would produce a magnetic field twice the strength of the Earth's magnetic field at a distance of 5.0 cm from the wire. To find this, we use Ampère's Law and the formula for the magnetic field around a long straight conductor, which is B = (u0*I)/(2*π*r), where B is the magnetic field, u0 is the permeability of free space (4*π*10⁻· T*m/A), I is the current, and r is the distance from the wire. The Earth's magnetic field's strength (bearth) is provided as 2 × 10⁻⁵ tesla (T).
To calculate the current needed to create a magnetic field twice that of the Earth's at 5.0 cm from the wire, the following steps are taken:
- First, double the Earth's magnetic field strength to find the target magnetic field: 2 × bearth = 4 × 10⁻⁵ T.
- Then, rearrange the formula to solve for the current I: I = B*2*π*r/u0.
- Lastly, insert the known values (B = 4 × 10⁻⁵ T, r = 0.05 m, u0 = 4*π*10⁻⁷ T*m/A) into the equation and calculate the current.
Note that the result should be stated only to two digits, based on the given accuracy of the Earth's magnetic field strength.