Question

Прямокутна рамка зі струмом знаходиться в неоднорідному магнітному полі. Доведіть, що сили Ампера, які діють на сторони рамки, втягують її в область більш сильного поля. помогите пожалуйста очень срочно​

Answer 1

На дві сторони діють сили Ампера, однакові за величиною та протилежні за напрямком

Тому R = F2 - F1 = 0H

Answer 2

To prove that the Ampere forces acting on the sides of a rectangular loop with current in a non-uniform magnetic field pull it into the region of stronger field, we can use the following reasoning:

Ampere's Law

Ampere's Law states that the magnetic field around a closed loop is directly proportional to the current passing through the loop. Mathematically, it can be expressed as:

∮ B · dl = μ₀ · I_enc

Where: - ∮ B · dl represents the line integral of the magnetic field B around a closed loop, - μ₀ is the permeability of free space, - I_enc is the total current enclosed by the loop.

Magnetic Field in a Non-Uniform Field

In a non-uniform magnetic field, the magnetic field strength varies at different points. This means that the magnetic field lines are closer together in regions of higher field strength and farther apart in regions of lower field strength.

Ampere Forces on the Sides of the Loop

When a current-carrying loop is placed in a non-uniform magnetic field, the Ampere forces act on the sides of the loop. These forces are perpendicular to both the current direction and the magnetic field direction. According to the right-hand rule, the Ampere forces on the sides of the loop will be directed towards the region of stronger magnetic field.

Proof

Let's consider a rectangular loop with current I and sides of length a and b. The loop is placed in a non-uniform magnetic field, where the magnetic field strength is stronger on one side of the loop compared to the other side.

1. The Ampere forces acting on the sides of the loop are given by the equation:

F = I · (L × B)

Where: - F is the force acting on the side of the loop, - I is the current passing through the loop, - L is the length of the side of the loop, - B is the magnetic field strength.

2. Since the magnetic field is stronger on one side of the loop, the force on that side will be greater than the force on the other side.

3. As a result, the net force on the loop will be directed towards the region of stronger magnetic field, causing the loop to be pulled into that region.

Therefore, we have proved that the Ampere forces acting on the sides of a rectangular loop with current in a non-uniform magnetic field pull it into the region of stronger field.

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