In a plane perpendicular to the magnetic field, the intensity

On a plane perpendicular to a magnetic field of intensity 100 A/m, there is a rectangular conductor 1 m long, which rotates around an axis passing through one of its ends. A current with a force of 10 A flows along the conductor, and the angular velocity of rotation is 50 s^-1. It is required to determine the work performed by the conductor in 10 minutes.

First, let's find the magnetic moment of the conductor. For a rectangular conductor, the magnetic moment is determined by the formula: M = abI, where a and b are the sides of the rectangle, I is the current strength in the conductor.

M = 1110 = 10 A*m^2

Then we find the moment of forces acting on the conductor. To do this, we use the formula: M = BMsin(α), where B is the magnetic induction, α is the angle between the direction of the magnetic field and the normal to the conductor.

Since the conductor rotates perpendicular to the magnetic field, then α = 90°, and sin(α) = 1. Then M = B*M.

The magnetic moment of the conductor is constant, and the magnetic induction in this case also does not change, so the moment of force will also be constant: M = 100101 = 1000 N*m.

Finally, we can calculate the work of the conductor in 10 minutes using the formula: A = MohΔt, where ω is the angular velocity of rotation of the conductor, Δt is the rotation time.

A = 100050(10*60) = 3,000,000 J = 3 MJ

Thus, the conductor performed 3 MJ of work in 10 minutes of rotation.

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Description: In a plane perpendicular to a magnetic field of intensity 100 A/m, a rectangular conductor 1 m long rotates about an axis passing through the end of the conductor. A current of 10 A is passed through the conductor, the angular velocity of rotation of the conductor is 50 s^-1. This product will allow you to study in more detail the laws of electromagnetism and their application in practice.

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Product description:

We present to you the digital product “The Laws of Electromagnetism”, which will allow you to gain access to unique information, expand your knowledge and skills in the field of electromagnetism. Our product contains a detailed description of the basic laws of electromagnetism, their application in practice, as well as many tasks and examples to consolidate the acquired knowledge.

In particular, in our product you will find a detailed solution to problem 31173, in which you need to determine the work of rotation of a conductor in a magnetic field. The solution uses the Biot-Savart-Laplace law to calculate the moment of forces, as well as formulas to calculate the magnetic moment of the conductor and the work of rotation. The solution is accompanied by a brief recording of the condition, the derivation of the calculation formula and the answer.

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This product is a rectangular conductor that can rotate in a plane perpendicular to a magnetic field of 100 A/m. The conductor has a length of 1 m and a current of 10 A is passed through it. The angular velocity of rotation of the conductor is 50 s^-1.

To solve the problem, it is necessary to determine the work of rotation of the conductor in 10 minutes. To do this you can use the formula:

W = ΔE = (1/2)Iω^2

where W is work, ΔE is the change in kinetic energy, I is the moment of inertia, ω is the angular velocity.

The moment of inertia of a rectangular conductor can be calculated using the formula:

I = (1/12)m(a^2+b^2)

where m is the mass of the conductor, a and b are the dimensions of the sides of the rectangle.

To determine the mass of the conductor, you can use the formula:

m = ρV

where ρ is the density of the conductor material, V is its volume.

Using Lorentz's law, we can calculate the force acting on the conductor:

F = BIL

where B is magnetic induction, L is the length of the conductor.

Then, using Newton's second law, the acceleration of the conductor and therefore the angular acceleration can be calculated:

a = F/m

α = a/R

where R is the radius of the circle along which the conductor moves.

By substituting the found values ​​into the formula for work, you can determine its value in 10 minutes.

This product is a problem to solve, not a physical item. The description of the task is already given in the text.

So, there is a straight conductor with a length of l = 1 m, through which a current of force I = 10 A flows. The conductor rotates in a plane perpendicular to a magnetic field of strength H = 100 A/m, with a frequency n = 50 rps. The axis of rotation passes through one of the ends of the conductor.

It is required to determine the work done by the field during time t = 10 minutes.

To solve the problem, it is necessary to use the formula to determine the magnetic induction on the axis of a rotating conductor: B = μ0*I/(2πr),

where μ0 is the magnetic constant, r is the distance from the axis of rotation to the conductor.

Then you need to find the moment of force acting on the conductor: M=BlI*sin(φ),

where φ is the angle between the magnetic induction vector and the normal to the plane of rotation of the conductor.

And finally, the work done by the field during time t can be found using the formula: A = M2πnt.

Laws used: Biot-Savart-Laplace law, law of interaction of magnetic fields.

Answer to the problem: A = 6.3 J.

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