A soft-iron toroid is concentric with a long straight conductor carrying a direct current \(I\). If the relative permeability \(\mu_r\) of soft-iron is 100, the ratio of the magnetic flux densities at two adjacent points located just inside and just outside the toroid, is ________ .
Solution
The magnetic field is generated by the long straight conductor. Let the two points be at approximately the same radial distance \(r\).
The flux density inside the toroid (soft-iron, \(\mu = \mu_0 \mu_r\)) is:
Equation
\[B_{\text{in}} = \frac{\mu_0 \mu_r I}{2\pi r}\]
The flux density just outside the toroid (air, \(\mu = \mu_0\)) is:
A rotating conductor of 1m length is placed in a radially outward (about the z-axis) magnetic flux density (\(B\)) of 1 Tesla as shown in figure below. Conductor is parallel to and at 1m distance from the z-axis. The speed of the conductor in r.p.m. required to induce a voltage of 1V across it, should be ________ .
Rotating conductor configuration
Solution
The induced EMF (Voltage) for a conductor cutting magnetic field lines is given by:
A parallel plate capacitor field with two dielectrics is shown in the figure below. If the electric field in the region A is 4 kV/cm, the electric field in the region B, in kV/cm, is:
Capacitor with two dielectrics
1
2
4
16
Solution
The figure shows two dielectrics placed side-by-side (parallel arrangement) between the two parallel plates.
The potential difference (\(V\)) across both regions is the same (connected to the same plates).
The distance (\(d\)) between the plates is the same for both regions.
The Electric Field is given by:
Equation
\[E = \frac{V}{d}\]
Since both \(V\) and \(d\) are constant for region A and region B:
