To semi infinite solenoid place the next each other separated by small gap of with WH shown the current I not in the solenoid flows in directions if the solenoids have circular cross section of radius R and filled with magnetic material of permeability mue when magnetic energy density inside the solenoid and UG in the gap are related as?

Question

Answer

Magnetic Energy Density in Solenoids
The magnetic energy density in a solenoid filled with a magnetic material and in the gap between solenoids can be understood through the concepts of magnetic field strength and permeability.

Magnetic Energy Density in the Solenoid
- The magnetic energy density $ u $ within the solenoid can be expressed as:
$$
u = \frac{B^2}{2\mu}
$$
- Here, $ B $ is the magnetic flux density, and $ \mu $ is the permeability of the magnetic material inside the solenoid.
- The magnetic flux density $ B $ can also be related to the current $ I $ and the number of turns per unit length $ n $ of the solenoid using:
$$
B = \mu n I
$$
- Substituting for $ B $ gives:
$$
u = \frac{(\mu n I)^2}{2\mu} = \frac{\mu n^2 I^2}{2}
$$

Magnetic Energy Density in the Gap
- In the gap between the solenoids, the magnetic energy density $ u_g $ is given by:
$$
u_g = \frac{B_g^2}{2\mu_0}
$$
- Here, $ B_g $ is the magnetic flux density in the gap and $ \mu_0 $ is the permeability of free space.
- Assuming the field in the gap is primarily due to the solenoids, it can be approximated as $ B_g \approx B $ since the solenoid fields extend into the gap.
- Thus, the expression becomes:
$$
u_g = \frac{B^2}{2\mu_0}
$$

Relation Between Energy Densities
- The energy densities in the solenoid and the gap can be compared through their respective equations.
- Given that the permeability of the magnetic material $ \mu $ is typically much greater than $ \mu_0 $, we find:
$$
u \gg u_g
$$
- This indicates that the magnetic energy density is significantly higher within the solenoid compared to the gap, reflecting the material's influence on the magnetic field.

Similar Physics Doubts

A long straight solenoid hasnturns per unit length. An alternating currentI=Imsinωtflows through it. Find the displacement current density as a function of distancerfrom the solenoid axis. The cross-sectional radius of solenoid equalsR.

A short solenoid with n turns per unit length has diameter D and length L=8D/15 as shown in the figure, and its carries a constant current I the magnetic field B at point P on the axis of the solenoid at a distance H=2D/3 from its near end is?

A long solenoid is carrying a time dependent current such that the magnetic field inside has the form B() = B,r'k, where k is along the axis of the solenoid. The displacement current at the point P on a circle of radiusr in a plane perpendicular to the axis (

Top Courses for Physics

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams