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Physics ys cs 132: 3 Lecture ectu e 20 0 Elements of Physics II A Agenda d for f T Today d Forces on currents Currents are moving charges Torque on current loop Torque on rotated loop Currents create B B--fields Adding magnetic fields Force between wires Physics 202: Lecture 9, Pg 1 The Magnetic Force on a Moving Charge The magnetic force turns out to depend not only on the charge and the charge’s velocity, but also on how the velocity vector is oriented relative to the magnetic field field. Physics 202: Lecture 9, Pg 2 The Magnetic Force on a Moving Charge The magnetic force turns out to depend not only on the charge and the charge’s velocity, but also on how the velocity vector is oriented relative to the magnetic field field. Physics 202: Lecture 9, Pg 3 The Magnetic Force on a Moving Charge The magnetic force turns out to depend not only on the charge and the charge’s velocity, but also on how the velocity vector is oriented relative to the magnetic field field. Physics 202: Lecture 9, Pg 4 Force on charged particle by BB-field The magnetic force on a charge q as it moves through a magnetic field B with velocity v is: where is the angle between v and B. Physics 202: Lecture 9, Pg 5 Flat Right Hand Rule To find the direction of the force felt by a charged particle moving in a magnetic-field ti fi ld Thumb = velocity Fingers = B-field. Palm = force If charge is negative force is opposite! Physics 202: Lecture 9, Pg 6 Examples Physics 202: Lecture 9, Pg 7 Give it a try: The direction of the magnetic force on the proton is A. B B. C. D D. E. To the right. T the To th left. l ft Into the screen. O t off the Out th screen. The magnetic force is zero. Physics 202: Lecture 9, Pg 8 M ti off q in Motion i uniform if B field fi ld Calculate R 2 v F m R v2 qvBsin θ m qvBsin R x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x R F v v x x x F • Force is perpendicular to B,v • Uniform circular motion • B does no work! • (W=F d cos ) • Speed is constant • (W= K.E. ) x x x x x x x x x Uniform B into p page g x x x x x x x mv R qB 35 Physics 202: Lecture 9, Pg 9 Clicker Question 8: A magnetic field B= 1.3×10 1 3×10-33 T pointing directly into the screen is used to protect a wall from damage due to incident particles of mass m = 3×10-27 kg, 19 C, and velocity v = positive charge q = 1.6×10-19 2×104 m/s as shown. What must the length L be? ((a)) About Ab t 15 cm (b) About 30 cm (c) About 60 cm (d) About 90 cm (e) About 100 cm Particle L? Physics 202: Lecture 9, Pg 10 Example L=R (3 10-27 kg) ( 2 10 4 m/s) mv R (1.6 10-19 C)(1.3 10-3 T) qB Particle .2885m R=L L? Physics 202: Lecture 9, Pg 11 Particle Moving in an External B-Field If the particle’s velocityy is not perpendicular to the field, the path followed by the particle is a spiral The spiral p p path is called a helix Physics 202: Lecture 9, Pg 12 Force on a Current F = q v B sin() Out of the page (RHR) • F =(q/t)(vt)B sin() = I L B sin() Flat right hand rule + v B + + + +v I = q/t L = vt Physics 202: Lecture 9, Pg 13 Give it a try: The horizontal wire can be levitated – held up against the force of gravity – if the current in the wire is A. Right to left. B. Left to right. C. It can’t be done with this magnetic field. Physics 202: Lecture 9, Pg 14 No Magnetic g Charges g Magnetic Fields are created by moving electric charge! Where is the moving charge? Orbits of electrons about nuclei Intrinsic “spin” of electrons (more important effect) Physics 202: Lecture 9, Pg 15 The Electron Spin An electron’s inherent magnetic moment is often called the electron spin because, because in a classical picture, a spinning ball of charge would have a magnetic moment. While it ma may not be spinning in a literal sense sense, an electron really is a microscopic magnet. Physics 202: Lecture 9, Pg 16 Magnetic Properties of Matter For most elements, the magnetic moments of th atoms the t are randomly arranged when the atoms join together to form a solid. As the figure shows, this random arrangement produces a solid whose net magnetic moment is very close to zero. Physics 202: Lecture 9, Pg 17 Ferromagnetism In iron, and a few other substances, the atomic magnetic moments tend to all line up in the same direction, as shown in the figure. g Materials that behave in this fashion are called ferromagnetic, with the prefix ferro meaning “iron-like iron like.” Slide 32-158 Physics 202: Lecture 9, Pg 18 Ferromagnetism A typical piece of iron is divided into small regions, typically less than 100 m in size, called magnetic domains. The magnetic moments of all the iron atoms within each domain are perfectly aligned aligned, so each individual domain is a strong magnet. However, the various magnetic domains that form a larger solid are randomly d l arranged. d Physics 202: Lecture 9, Pg 19 Induced Magnetic Dipole If a ferromagnetic substance is subjected to an external magnetic field field, the external field exerts a torque on the magnetic dipole of each domain. q causes The torque many of the domains to rotate and become aligned li d with ith th the external field. Physics 202: Lecture 9, Pg 20