- #1

- 107

- 38

- Homework Statement
- What voltage is induced in the bent wire

- Relevant Equations
- none

Hi,

unfortunately, I am not sure if I have calculated the task correctly here

Task a

I have now proceeded in such a way that I thought that the magnetic field only flows through the area drawn in red. Which ##\frac{1}{4}## corresponds to the area of a circle.

By the fact that the magnetic field is constant and points in direction x, that the magnetic field is parallel to the normal vector of the surface. Then the following applies ##\vec{B} \cdot d \vec{A}=B \cdot dA##.

Then the magnetic flux is as follows

$$\phi =\int_{}^{} B dA=\frac{1}{4} \pi r^2 B$$

The induced voltage is then calculated as

$$\frac{d \phi}{dt}=\frac{1}{4} \pi r^2 \frac{dB}{dt}=\frac{1}{4} \pi (0.1m)^2 5 \frac{mT}{s}=3.92*10^{-5} V $$

Task b

The induced current always flows in such a way that an opposing magnetic field is generated to neutralize the changing external magnetic field, which means that the current in the NO segment must flow clockwise.

I am not sure if I have solved the problem a correctly, because does the magnetic flux also flow, through the blue colored surface, which corresponds to the surface of a ##\frac{1}{8}## a sphere.

The magnetic field is constant in x-direction, that means the normal vector of the surface and the magnetic field is not parallel to each other and therefore the calculation would be much more complicated.

unfortunately, I am not sure if I have calculated the task correctly here

Task a

I have now proceeded in such a way that I thought that the magnetic field only flows through the area drawn in red. Which ##\frac{1}{4}## corresponds to the area of a circle.

By the fact that the magnetic field is constant and points in direction x, that the magnetic field is parallel to the normal vector of the surface. Then the following applies ##\vec{B} \cdot d \vec{A}=B \cdot dA##.

Then the magnetic flux is as follows

$$\phi =\int_{}^{} B dA=\frac{1}{4} \pi r^2 B$$

The induced voltage is then calculated as

$$\frac{d \phi}{dt}=\frac{1}{4} \pi r^2 \frac{dB}{dt}=\frac{1}{4} \pi (0.1m)^2 5 \frac{mT}{s}=3.92*10^{-5} V $$

Task b

The induced current always flows in such a way that an opposing magnetic field is generated to neutralize the changing external magnetic field, which means that the current in the NO segment must flow clockwise.

I am not sure if I have solved the problem a correctly, because does the magnetic flux also flow, through the blue colored surface, which corresponds to the surface of a ##\frac{1}{8}## a sphere.

The magnetic field is constant in x-direction, that means the normal vector of the surface and the magnetic field is not parallel to each other and therefore the calculation would be much more complicated.