Question

Магнитная индукция поля в точке, расположенной на расстоянии 15 см от прямого бесконечно длинного проводника, равна 30 мкТл. Найти силу тока в этом проводнике, используя теорему о циркуляции вектора B.

Answer 1

Ответ:

надеюсь что я тебя хот мимног памог

Answer 2

Calculation of Current using the Circulation Theorem

To find the current in the wire using the circulation theorem, we need to know the magnetic field induction at a point located 15 cm away from the wire. According to the given information, the magnetic induction at that point is 30 μT.

The circulation theorem states that the line integral of the magnetic field around a closed loop is equal to the product of the current passing through the loop and the permeability of free space (μ₀).

Mathematically, the circulation theorem can be expressed as:

∮ B · dl = μ₀ * I

Where: - ∮ B · dl is the line integral of the magnetic field B around a closed loop - μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A) - I is the current passing through the loop

In this case, we have a straight, infinitely long wire, and we want to find the current passing through it. Let's assume we choose a circular loop with a radius of 15 cm centered on the wire. The line integral of the magnetic field around this loop is equal to the product of the magnetic field induction and the circumference of the loop.

∮ B · dl = B * 2π * r

Where: - B is the magnetic field induction (30 μT) - r is the radius of the loop (15 cm or 0.15 m)

Substituting the values into the equation, we get:

B * 2π * r = μ₀ * I

Simplifying the equation, we can solve for the current:

I = (B * 2π * r) / μ₀

Let's calculate the current using the given values:

I = (30 μT * 2π * 0.15 m) / (4π × 10⁻⁷ T·m/A)

Simplifying further:

I = (30 * 2 * 0.15) / (4 × 10⁻⁷) A

I ≈ 2.25 × 10⁵ A

Therefore, the current in the wire is approximately 2.25 × 10⁵ A.

Please note that the above calculation assumes that the wire is an ideal conductor with negligible resistance and that the magnetic field is uniform around the loop.