{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 9 - Magnetic Forces, Materials and Inductance

# Chapter 9 - Magnetic Forces, Materials and Inductance -...

This preview shows pages 1–14. Sign up to view the full content.

Chapter 9 Magnetic Forces, Materials, and Inductance Magnetic Forces, Materials, and Inductance Physical significance of Chapter 8 Magnetic forces and torques Magnetic materials Inductance

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
In electrostatics, E causes a force to be exerted on a charge (either stationary or moving) In steady magnetic fields, H causes a force to be exerted ONLY on moving charges. Force on a Moving Charge
Force on a Moving Charge In electrostatics, F = Q E Given a charged particle in motion in a magnetic field of flux density B , Force exerted on this particle F = Q v x B Where v = velocity of charge Note: The acceleration vector is always normal to v .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Trajectory of a moving electron in a region with magnetic field.
Thus, the magnitude of velocity is unchanged. There is no change in kinetic energy. Therefore, H is incapable of transferring energy to the moving charge. If both E and B are present, F = Q ( E + ( v x B )) Lorentz Force Equation

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: Cyclotron The cyclotron uses electric and magnetic fields to accelerate charged particles
d F = dQ v x B d F = ρ v dv v x B Force on a Differential Current Element the force due to H is exerted on moving charges confined in the conductor in effect, this force is collectively transferred to the conductor itself Since J = ρ v v , d F = J x B dv

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
d F = J x B dv J dv = K dS = I dL dF = K x B dS dF = I d L x B × - = × = L B B L F d I Id For a closed circuit: Over the entire volume or surface: dv vol B J F × = × = s dS B K F
For a straight conductor in a uniform magnetic field: F = I L x B I F I = F = B I L sin θ dF = I d L x B

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Consider a square loop of wire and a current-carrying filament H due to filament at the xy-plane: m A x 2 15 x 2 I z z a a π = π = H H B 7 0 10 4 - × π = μ = T x 10 3 6 z a - × =
What is F on the loop? × - = L B F d I loop pN 8 ) dy ( 1 ) dx ( x ) dy ( 3 ) dx ( x 10 3 mA 2 2 0 y 3 1 x 2 0 y 3 1 x 6 x y z x z y z x z a a a a a a a a a F - = - × + - × + × + × - = = = = = - T x 10 3 6 z a B - × =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Given two differential current elements at points 1 & 2, 2 2 2 2 2 2 2 2 2 12 1 1 2 d d I ) d ( d d I d R 4 d I d B L F B L F a L H r12 × = × = π × = I 2 d L 2 I 1 d L 1 R 1 2 Force Between Differential Current Elements
2 12 1 1 0 2 2 R 4 x d I d I π μ × = 12 R a L L ( ) [ ] 12 R a L L x d x d R 4 I I 1 2 2 12 2 1 0 π μ = 2 2 12 1 2 1 0 d R d a 4 I I L L 12 R × × π μ =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}