Question

1. Два одинаковых круговых витка с общим центром расположены во взаимно перпендикуляр­ных плоскостях. Когда сила тока в витках одинако­ва, индукция магнитного поля в центре витков рав­на Bо. Найти индукцию магнитного поля в той же точке, когда ток течет лишь по одному проводнику.

Answer 1

Так как вектора магнитной индукции витков расположены под углом 90 градусов то по теореме Пифагора
Bo= √B1²+B2²

по условию токи равны значит B1=B2
Bo=√2*B1²=B1*√2

B1=B2=Bo/√2

Ответ B1=Bo/√2=Bo/1.4

Answer 2

Calculation of Magnetic Field Induction

To find the magnetic field induction at a point when the current flows through only one conductor, we can use the principle of superposition. The principle of superposition states that the total magnetic field at a point due to multiple current-carrying conductors is the vector sum of the magnetic fields produced by each individual conductor.

Let's assume that the two circular loops have the same radius and are perpendicular to each other. The current flowing through each loop is the same, and the magnetic field induction at the center of the loops is Bo.

To find the magnetic field induction at the same point when the current flows through only one conductor, we can consider the magnetic field produced by each loop separately and then add them together.

Let's denote the magnetic field induction produced by the first loop as B1 and the magnetic field induction produced by the second loop as B2.

Since the loops are identical and the current flowing through each loop is the same, the magnetic field induction produced by each loop will also be the same. Therefore, B1 = B2 = Bo.

According to the principle of superposition, the total magnetic field induction at the center of the loops when the current flows through only one conductor is the vector sum of B1 and B2.

The vector sum of two vectors of the same magnitude and in perpendicular directions is given by the square root of the sum of their squares. Therefore, the total magnetic field induction at the center of the loops when the current flows through only one conductor is:

B = sqrt(B1^2 + B2^2)

Substituting B1 = B2 = Bo, we get:

B = sqrt(Bo^2 + Bo^2) = sqrt(2Bo^2) = sqrt(2) * Bo

Therefore, the magnetic field induction at the same point when the current flows through only one conductor is sqrt(2) * Bo.

Please note that this calculation assumes ideal conditions and neglects any effects such as the finite size of the conductors or the presence of other nearby conductors that may affect the magnetic field.