Electromotive force induced in rotating coil¶
Suppose a coil is being rotated around the axis that lies in the coil’s cross section (see Figure) in a magnetic field under the conditions described below. Then an electromotive will be induced in the contour of the coil. Its amplitude depends on the number of turns in the coil, the magnetic flux density, the angular frequency of the coil’s rotation and the area of the coil’s contour.
Notes:
The angle \(\varphi\) between the normal to the coil’s contour and the magnetic flux density is \(\varphi \propto \cos(\omega t)\). See Figure.
Conditions:
The magnetic field is uniform.
The angular velocity of the coil’s rotation is orthogonal to the magnetic field.
The area of the coil’s contour is constant.
The angular speed of the coil’s rotation constant.
- electromotive_force¶
electromotive_forceinduced in the coil.- Symbol:
E- Latex:
\(\mathcal{E}\)
- Dimension:
voltage
- coil_turn_count¶
Number of turns in the coil. See
positive_number.- Symbol:
N- Latex:
\(N\)
- Dimension:
dimensionless
- magnetic_flux_density¶
-
- Symbol:
B- Latex:
\(B\)
- Dimension:
magnetic_density
- contour_area¶
Cross-sectional
areaof the contour enclosed by the coil.- Symbol:
A- Latex:
\(A\)
- Dimension:
area
- angular_frequency¶
angular_frequencyof the coil’s rotation.- Symbol:
w- Latex:
\(\omega\)
- Dimension:
angle/time
- law¶
E = -N * B * A * w * sin(w * t)- Latex:
- \[\mathcal{E} = - N B A \omega \sin{\left(\omega t \right)}\]