I need the answer quickly 8.1 INTRODUCTION8.2 FORCES DUE TO MAGNETIC FIELDSThere are at least three ways in which force due to magnetic fields can be experienced, The forcecan be [2].• due to anarticle in a B field,na current element in an extenLorbetween two current elements.8.2.1 Force on a Charged Particle (Moving Charge)In chapter two, we discussed that the electric force F, on a stationary o oving electric charge Qin an electric field is given by Coulomb's law and is related to the electri eld intensity E as (2):F = QE(8.1)that if Q is positive, F and E have the samon and F, is directly proportionalto both E and QTIA magnetic field can exert force only on a moving charge. From experiments, it is found that themagnetic force Fm experienced by a charge Q moving with a velocity u in a magnetic field B is[2):F = Qu x B(8.2)%3DThe force F has direction perpendicular to both u and B and whose magnitude is proportionalto the product of the magnitudes of the charge Q, its velocity u, the flux density B, and to thesine of the angle between the vectors u and B [1].-.A comparison between the electric force and the magnetic force can be made [2].• The electric force F, is independent of the velocity of the charge.• The electric force E can perform work on the charge and change its kinetic energy.The magnetic force F depends on the charge velocity and is normal to it.• The magnetic force F cannot perform work because it is at right angles to the directionof motion of the charge (Fn dL = 0); it does not cause an increase in kinetic energy ofthe charge.The magnitude of E is generally small compared to F, except at high velocities.31Chapter 8:Magnetic Forces, Materials, and DevicesFor a moving charge Q in the presence of both electric and magnetic fields, the total force on thecharge is given by superposition [2].F = F, + E = Q E+ Qu x BF = Q (E + ux B)(8.3)This equation is known as the Lorentz force equation, and its solution is required in determiningelectron orbits in the magnetron, proton paths in the cyclotron, plasma characteristics in amagneto-hydrodynamic (MHD) generator, or, in general, charged-particle motion in combinedclectric and magnetic fields | 1).Lorentz force equation relates mechanical force to electrical force. If the mass of the charged.particle moving in E and B fields is (m), by Newton's second law of motion [2].duF =m = ma = Q (E + ux B)dt(8.4)Table (8.1) Force on a Charged ParticleNo.State of Die FieldMagnetic FieldCombined E and B FieldsstationaryQEQE----MovingQEQ (E +ux B)8.2.2 Force on a Differential Current Element.The force on a charged particle moving through a steady mae field may be written as theLforce exerted on a differentialCarge |1).dF = dQu x B(8.5)The force on a current element (IdL) of a current-carrying conductor due to the magnetic field,can be determined by using the fact that for convection current density [2]:

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The field (magnetic) on a moving charge is one of the most key knowns. Magnetic force is just about…

3.2.1 Force on a Charged Particle (Moving Charge) In chapter two, we discussed that the electric force F, on a stationary o oving electric charge Q n an electric field is given by Coulomb's law and is related to the electr cld intensity E as (21: F= QE (8.1)