Magnetic f ields

1. Magneticfields Bytheend of thischapteryoushouldbeableto: understandthemeaning of magneticfied and finditsmagnitude and direction in simple situationsinvolvingstright-line conductors and solenoidsusingtheright-hand rule whereappropriate; findtheforceonmovingcharges and currents in magneticfields and appreciatethedefinition of the ampere as a fundamental SI unit, usingtheright-hand rule forforceswhereappropriate.

2. Magneticfield Bothmagnets and electriccurrentscreatemagneticfieldsaroundthemselves and whenanothermagnetorelectriccurrent (ormovingchargein general) entersthismagneticfielditwillexperience a magneticforce. Themagneticfieldis a vector quantityjustliketheelectricfield.

3. Thedirection of themagneticfield Themagneticfielddirectionisdeterminedbytheeffectit has on a compassneedle. A magneticneedlealignsitself in thedirection of themagneticfield vector.

4. Magneticfieldlines Justlikeelectricfieldlines, magneticfieldlines are defined as imaginarylinesaroundmagnets and currents, tangentstowhichgivethedirection of themagneticfield. Magneticfieldlines of permanentmagnets Magneticfieldlinescreatedby a solenoid

5. Magneticfieldlines Themagneticfieldlines of a single turn of wire Magneticfieldlinesfor a straightcurrentwire

6. Themagneticforceon a current If a currentis placed in a region of magneticfield, itwillexperience a magneticforce. Themagnitude of theforceisproportionaltothecurrentI, themagneticfieldmagnitudeB and thelenthL of thewirethatis in themagneticfield. Theforceon a lenghtL of thewireisgivenby F = BIL sinθ, whereθistheanglebetweenthecurrent and thedirection of themagneticfield. Thedirection of themagneticforceisalways normal toboththecurrent and themagneticfied.

7. Themagneticforceon a movingcharge Anelectriccurrentthatis in a magneticfieldwillexperience a force. Butanelectriccurrentisjustmovingcharges, so a movingchargewillexperience a magneticforce as well. Consider a positive chargeqthatmoveswithspeedvtotheright. In time Δtthechargewillmove a distanceL = v Δt. ThecurrentcreatedbythischargeisI=q/Δt, so theforceonthiscurrentis F = BIL sinθ = B(q/Δt)vΔt sinθ =qvB sinθ Thisimpliesthatthemagneticforceiszeroifthechargemovesparallelorantiparalleltothemagneticfield. Thereisalso no magneticforceifthechargeisnotmoving. Themagneticforceonparticlesthat are electrically neutral iszero.

8. Orsted’sdiscovery Themagnitude of themagneticfield B createdbythecurrent in a wirevarieslinearlywiththecurrent in thewire and inverselywiththe perpendicular distancefromthewire. B = μ0 I/(2πr) μ0= 4π x 10-7 Tm/A (magneticpermeability of vacuum)

9. Orsted’sdiscovery Themagneticfieldstrength B at the centre of a circular loop of radius R carryingcurrent I is In the interior of thesolenoidthemagneticfieldisuniform in magnitude and direction and isgivenby B = μ0 NI/L. A muchstrongermagneticfield can beobtainedifthesolenoid has anironcore.

10. Theforcebetweentwocurrent-carryingwires Considertwolong, straight, parallelwireseachcarryingcurrent, sayI1 and I2. Thefirstwire (1) creates a magneticfield in space, and in particular at the position of thesecondwire (2). Thus, wire 2 willexperience a magneticforce. Similarly, wire 2 will produce a magneticfield a the position of wire 1, so thatwire 1 willalsoexperience a magneticforce. ByNewton’sthirdlaw, theforcesexperiencedbythetwowires are equal and opposite. Ifthecurrents are parallel, theforces are attractive and ifthey are antiparallel, theforces are repulsive.

11. Theforcebetweentwocurrent-carryingwires Thewire 1 creates a magneticfieldB1 and thewire 2 a magneticfieldB2. Thismeansthatwire 2 in themagneticfield of wire 1 (B1), and so willexperience a force. Similarly, wire 1 is in themagneticfield of wire 2 (B2), and so ittoowillexperience a force. Ifthetwoparallelwires are separatedby a distance r, then Now, theforceon a length L of wire 2 is and similarlytheforceonanequallength of wire 1 is

12. Ampere definition The ampere isdefinedthroughthemagneticforcebetweentwoparallelwires. Iftheforceon a 1 m length of twowiresthat are 1 m apart and carryingequalcurrentsis 2 x 10-7 N, thenthecurrent in eachewireisdefinedtobe 1 A.