Question

В магнитное поле индукцией В = 0,1 Тл помещен контур, выполненный в форме кругового витка радиусом R = 3,4 см. Виток сделан из медной проволоки, площадь поперечного сечения которой S = 1 мм2. Нормаль к плоскости витка совпадает с линиями индукции поля. Какой заряд пройдет через поперечное сечение витка при исчезновении поля?

Answer 1

DФ/dt=B*pi*r^2/dt=U=I*R=I*ro*L/S=I*ro*2*pi*r/S
B*pi*r^2/dt=I*ro*2*pi*r/S
Q=I*dt=B*pi*r^2/(ro*2*pi*r/S)=B*r*S/(ro*2)=0,1*0,034*1/(2*0,017) Кл = 0,1 Кл

Answer 2

Calculation of the Charge Passing through the Cross-Section of the Coil

To calculate the charge passing through the cross-section of the coil when the magnetic field disappears, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced electromotive force (EMF) in a closed loop is equal to the rate of change of magnetic flux through the loop.

The magnetic flux through the loop can be calculated using the formula:

Φ = B * A

Where: - Φ is the magnetic flux - B is the magnetic field induction - A is the area of the loop

In this case, the magnetic field induction (B) is given as 0.1 T and the area (A) of the loop is the same as the area of the cross-section of the wire, which is given as 1 mm².

Converting the area to square meters: A = 1 mm² = 1 * 10^(-6) m²

Substituting the values into the formula, we get: Φ = 0.1 T * 1 * 10^(-6) m²

Now, to calculate the induced EMF, we can use the formula:

EMF = -dΦ/dt

Where: - EMF is the induced electromotive force - dΦ/dt is the rate of change of magnetic flux

Since the magnetic field is disappearing, the rate of change of magnetic flux is equal to the negative of the initial magnetic flux divided by the time it takes for the field to disappear.

Assuming the time taken for the field to disappear is t seconds, we have: dΦ/dt = -Φ/t

Substituting the values, we get: EMF = -(0.1 T * 1 * 10^(-6) m²) / t

The induced EMF is equal to the potential difference across the wire, which is equal to the charge passing through the wire divided by the resistance of the wire.

Assuming the resistance of the wire is R ohms, we have: EMF = Q / R

Rearranging the equation, we get: Q = EMF * R

Substituting the value of the induced EMF and the resistance of the wire, we get: Q = -(0.1 T * 1 * 10^(-6) m²) / t * R

Please provide the value of the resistance (R) and the time (t) for a more accurate calculation.