A square copper frame with a resistance of 5 Ohms is pushed halfway into the region of a magnetic field with an induction of 1.6 Tesla. The lines of magnetic induction are perpendicular to the plane of the frame. The side of the frame is 0.1 m. The frame performs harmonic oscillations in its plane in the direction perpendicular to the boundary of the magnetic field. The oscillation frequency is 50 Hz, and the oscillation amplitude is 0.05 m. It is necessary to determine the maximum value of the current induced in the frame. We neglect the magnetic field of the induced current.
Answer:
The induced current in the loop is caused by a change in the magnetic flux through it. Magnetic flux is related to the magnetic field induction as follows: $\Phi = B\cdot S\cdot\cos{\alpha}$, where $B$ is the magnetic field induction, $S$ is the frame area, $\alpha$ is the angle between the induction vector and the normal to the frame area.
During harmonic oscillations of the frame, the magnetic flux through it will change, which will lead to the induction of an electromotive force and, consequently, to the appearance of an induced current. The maximum value of the induced current is achieved at the moment when the speed of the frame is maximum and is equal to zero at the turning points.
The maximum speed of the frame is equal to $v_\text{max} = 2\pi f A$, where $f$ is the oscillation frequency, $A$ is the oscillation amplitude. Thus, the maximum value of the change in magnetic flux through the frame will be equal to $\Delta\Phi_\text{max} = B\cdot S\cdot\sin{\alpha}\cdot A$, where $\alpha$ is the angle between the induction vector and the direction of vibration of the frame.
Then the maximum value of the current induced in the frame will be equal to $I_\text{max} = \frac{\Delta\Phi_\text{max}}{R}$, where $R$ is the resistance of the frame. Substituting the known values, we get:
$I_\text{max} = \frac{B\cdot S\cdot\sin{\alpha}\cdot A}{R} = \frac{1,6\cdot0,1^2\cdot\sin{90^\circ}\cdot0,05}{5} \approx \underline{\underline{0,002\text{ А}}}$.
Introducing the 5 Ohm Square Copper Frame, a unique digital product that will allow you to study electromagnetism and conduct various experiments.
The frame has a side of 0.1 m and is made of high-quality copper, which ensures its long service life. It is half pushed into the region of a magnetic field with an induction of 1.6 Tesla and is capable of conducting harmonic oscillations in its plane in a direction perpendicular to the boundary of the magnetic field.
The magnetic induction lines are perpendicular to the plane of the frame, which makes it possible to study various effects associated with the interaction of the magnetic field and electric current.
This digital product is ideal for teaching schoolchildren and students, as well as for conducting scientific research in the field of electromagnetism.
Don't miss the opportunity to purchase a 5 Ohm square copper frame and expand your horizons in the field of electromagnetism!
A square copper frame measuring 0.1 m with a resistance of 5 ohms is presented, halfway pushed into the region of a magnetic field with an induction of 1.6 Tesla. The lines of magnetic induction are perpendicular to the plane of the frame. The frame performs harmonic oscillations in its plane in the direction perpendicular to the boundary of the magnetic field, with a frequency of 50 Hz and an amplitude of 0.05 m. It is necessary to determine the maximum value of the current induced in the frame, neglecting the magnetic field of the induced current.
To solve the problem, we use Faraday's law, according to which the induction of electromotive force in a conductor is proportional to the rate of change of the magnetic flux through it. The maximum value of the induced current is achieved at the moment when the speed of the frame is maximum and is equal to zero at the turning points.
The magnetic flux through the frame is related to the magnetic field induction as follows: $\Phi = B\cdot S\cdot \cos{\alpha}$, where $B$ is the magnetic field induction, $S$ is the area of the frame, $\alpha$ - the angle between the induction vector and the normal to the frame area.
During harmonic oscillations of the frame, the magnetic flux through it will change, which will lead to the induction of an electromotive force and, consequently, to the appearance of an induced current. The maximum speed of the frame is equal to $v_\text{max} = 2\pi f A$, where $f$ is the oscillation frequency, $A$ is the oscillation amplitude. Thus, the maximum value of the change in magnetic flux through the frame will be equal to $\Delta\Phi_\text{max} = B\cdot S\cdot\sin{\alpha}\cdot A$, where $\alpha$ is the angle between the induction vector and the direction of vibration of the frame.
Then the maximum value of the current induced in the frame will be equal to $I_\text{max} = \frac{\Delta\Phi_\text{max}}{R}$, where $R$ is the resistance of the frame. Substituting the known values, we get:
$I_\text{max} = \frac{B\cdot S\cdot\sin{\alpha}\cdot A}{R} = \frac{1,6\cdot0,1^2\cdot\sin{90^\circ}\cdot0,05}{5} \approx \underline{\underline{0,002\text{ А}}}$.
Thus, the maximum value of the current induced in the frame is 0.002 A. A square copper frame with a resistance of 5 Ohms can be used for conducting various experiments and studying electromagnetism, as well as for teaching schoolchildren and students.
A square copper frame with a resistance of 5 ohms is pushed halfway into the region of a magnetic field with an induction of 1.6 Tesla. The lines of magnetic induction are perpendicular to the plane of the frame, and its side is 0.1 m. The frame performs harmonic oscillations in its plane in the direction perpendicular to the boundary of the magnetic field, with a frequency of 50 Hz and an amplitude of 0.05 m. It is necessary to determine the maximum value of the current induced in the frame , neglecting the magnetic field of the induced current.
The induced current in the loop is caused by a change in the magnetic flux through it. Magnetic flux is related to the magnetic field induction as follows: $\Phi = B\cdot S\cdot\cos{\alpha}$, where $B$ is the magnetic field induction, $S$ is the frame area, $\alpha$ is the angle between the induction vector and the normal to the frame area.
During harmonic oscillations of the frame, the magnetic flux through it will change, which will lead to the induction of an electromotive force and, consequently, to the appearance of an induced current. The maximum value of the induced current is achieved at the moment when the speed of the frame is maximum and is equal to zero at the turning points.
The maximum speed of the frame is equal to $v_\text{max} = 2\pi f A$, where $f$ is the oscillation frequency, $A$ is the oscillation amplitude. Thus, the maximum value of the change in magnetic flux through the frame will be equal to $\Delta\Phi_\text{max} = B\cdot S\cdot\sin{\alpha}\cdot A$, where $\alpha$ is the angle between the induction vector and the direction of vibration of the frame.
Then the maximum value of the current induced in the frame will be equal to $I_\text{max} = \frac{\Delta\Phi_\text{max}}{R}$, where $R$ is the resistance of the frame. Substituting the known values, we get:
$I_\text{max} = \frac{B\cdot S\cdot\sin{\alpha}\cdot A}{R} = \frac{1,6\cdot0,1^2\cdot\sin{90^\circ}\cdot0,05}{5} \approx \underline{\underline{0,002\text{ А}}}.$
Thus, the maximum value of the current induced in the frame is 0.002 A. The square copper frame with a resistance of 5 ohms is a unique digital product that allows you to study electromagnetism and conduct various experiments. It is ideal for teaching schoolchildren and students, as well as for conducting scientific research in the field of electromagnetism.
***
A square copper frame has a side length of 0.1 m and a resistance of half 5 ohms. The frame is pushed into the region of a magnetic field with an induction of 1.6 Tesla, while the lines of magnetic induction are perpendicular to the plane of the frame.
The frame performs harmonic oscillations in its plane with a frequency of 50 Hz and an amplitude of 0.05 m. It is necessary to determine the maximum value of the current induced in the frame.
To solve the problem, we use Faraday’s law of electromagnetic induction:
?MDS = -dF / dt
where ?MDS is electromotive force, F is magnetic flux, t is time.
The magnetic flux through the frame area can be expressed as follows:
Ф = B * S * cos(a)
where B is the magnetic field induction, S is the area of the frame, α is the angle between the plane of the frame and the direction of the magnetic field.
Since the lines of magnetic induction are perpendicular to the plane of the frame, then α = 90°, and cos(α) = 0. Therefore, the magnetic flux through the frame is zero.
Consequently, ΔMDS induced in the frame is also zero. Consequently, the maximum value of the current induced in the frame will also be zero.
Answer: the maximum value of the current induced in the frame is zero.
***
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Quality material and fine workmanship are the excellent advantages of this copper frame.
It is great for creating various electronic circuits and prototypes.
This item is easy to integrate with other electronic components and sensors.
Half 5 ohm resistance makes this frame the perfect choice for many projects.
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The square copper frame is a great choice for beginners and experienced electronics engineers.
A large selection of sizes and shapes allows you to choose the perfect option for any project.
This item is great for teaching and research projects.
A square copper frame with a resistance of 5 ohms is an excellent choice for those who value quality and functionality.
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Solution K4-51 (Figure K4.5 condition 1 S.M. Targ 1989) - Переформулируем текст, сохраняя структуру HTML-кода.Решение К4-51Рассмотрим прямоугольную пластину ( ... ...