Calculate the magnitude of the magnetic field at a point 43.6 cm from a long, thin conductor carrying a current of 1.24 A. The permeability of free space is 1.25664 × 10^−6 T · m/A.
Answer in units of T
B=μ₀I/2πb=1.25664•10⁻⁶•1.24/2π•0.436 =5.69•10⁻⁷ T
Whoa, hold on to your magnets! Let's calculate the magnitude of the magnetic field at a point 43.6 cm away from our long, thin conductor. All you need is some current and a little bit of magic!
Using Ampere's Law, we can calculate the magnetic field using the formula:
B = (μ0 * I) / (2π * r)
Where:
B is the magnetic field,
μ0 is the permeability of free space (1.25664 × 10^−6 T · m/A),
I is the current (1.24 A), and
r is the distance from the conductor (43.6 cm).
Now, let's plug in those numbers and wave our magnet-wand to get the answer:
B = (1.25664 × 10^−6 T · m/A * 1.24 A) / (2π * 0.436 m)
B ≈ 1.127 × 10^-5 T
Voila! The magnitude of the magnetic field at a point 43.6 cm from the conductor is approximately 1.127 × 10^-5 Tesla (T). Keep those magnetic fields in check, and try not to attract too much attention!
To calculate the magnitude of the magnetic field at a point due to a long, thin conductor, you can utilize the formula:
B = (μ0 * I) / (2 * π * r)
Where:
B is the magnitude of the magnetic field,
μ0 is the permeability of free space (1.25664 × 10^−6 T · m/A),
I is the current passing through the conductor (1.24 A),
r is the distance from the conductor (43.6 cm = 0.436 m), and
π is a mathematical constant approximately equal to 3.14159.
Substituting the given values into the formula:
B = (1.25664 × 10^−6 T · m/A * 1.24 A) / (2 * 3.14159 * 0.436 m)
Calculating the result:
B ≈ (1.5677096 × 10^−6 T · m) / (2.716247892 m)
B ≈ 5.7691 × 10^−7 T
Therefore, the magnitude of the magnetic field at a point 43.6 cm from the current-carrying conductor is approximately 5.7691 × 10^−7 T.
To calculate the magnitude of the magnetic field at a point near a current-carrying conductor, you can use the formula for the magnetic field produced by a current-carrying wire, which is given by the equation:
B = (μ₀ * I) / (2π * r)
Where:
B is the magnitude of the magnetic field,
μ₀ is the permeability of free space (given as 1.25664 × 10^−6 T·m/A),
I is the current flowing through the wire, and
r is the distance from the wire to the point where you want to calculate the magnetic field.
Given that the current I is 1.24 A and the distance r is 43.6 cm (converted to meters, which is 0.436 m), we can substitute these values into the formula to find the magnitude of the magnetic field.
B = (1.25664 × 10^−6 T·m/A * 1.24 A) / (2π * 0.436 m)
Now we can simplify the equation:
B = (1.5623936 × 10^−6 T · m^2/A)/(2π * 0.436 m)
Simplifying further:
B = 1.5623936 × 10^−6 T · m^2 / (2π * 0.436 m)
B ≈ 1.795 × 10^−6 T
Therefore, the magnitude of the magnetic field at a distance of 43.6 cm from the current-carrying conductor is approximately 1.795 × 10^−6 T.