Dr. Jie ZouPHY Chapter 29 Magnetic Fields

Dr. Jie ZouPHY Outline Magnetic fields (29.1) Magnetic force on a charged particle moving in a magnetic field (29.1) Magnitude Direction: right-hand rule Magnetic force on a current-carrying conductor (29.2) Straight wire Curved wire Wire loop

Dr. Jie ZouPHY Magnetic fields Lifting fingerprints by a magnetic brush A spoon-shaped compass Magnetic field lines

Dr. Jie ZouPHY Magnetic force on a charged particle moving in a magnetic field Vector expression for the magnetic force on a charged particle moving in a magnetic field: F B = qv  B Magnitude of the magnetic force F B = |q|vB sin  If  = 0  or 180 , v // B, F B = 0. If  = 90 , v  B, F B is maximum. If v = 0, non-moving charge, F B = 0. Direction of the magnetic force? – use the right-hand rule. SI unit of B: the tesla (T); 1 T = 1 N/(C·m/s) Another unit in common use: gauss (G); 1 T = 10 4 G.

Dr. Jie ZouPHY Right-hand rule F B is  to both v and B; F B is  to the plane formed by v and B. To find the direction of F B = qv  B : (1) Find the direction of the cross product v  B, using the right-hand rule. Right-hand rule: Point the four fingers of your right hand along the direction of v and curl them toward B. The extended thumb points in the direction of v  B. (2) If q is “+”, F B is in the direction of your thumb; if q is “-”, F B is opposite the direction of your thumb.

Dr. Jie ZouPHY Quick Quiz An electron moves in the plane of this paper toward the top of the page. A magnetic field is also in the plane of the page and directed toward the right. The direction of the magnetic force on the electron is (a) toward the top of the page, (b) toward the bottom of the page, (c) toward the left edge of the page, (d) toward the right edge of the page, (e) upward out of the page, (f) downward into the page.

Dr. Jie ZouPHY Example 29.1 An electron moving in a magnetic field An electron in a television picture tube moves toward the front of the tube with a speed of 8.0 x 10 6 m/s along the x axis. Surrounding the neck of the tube are coils of wire that create a magnetic field of magnitude T, directed at an angle of 60  to the x axis and lying in the xy plane. Calculate the magnetic force on the electron. Find both the magnitude and direction of the force. (A) Use equation F B = qv  B. (B) Use a vector expression.

Dr. Jie ZouPHY Important differences between eclectic and magnetic forces The electric force acts along the direction of the electric field, whereas the magnetic force acts perpendicular to the magnetic field. The electric force acts on a charged particle regardless of whether the particle is moving, whereas the magnetic force acts on a charged particle only when the particle is in motion. The electric force does work in displacing a charged particle, whereas the magnetic force associated with a steady magnetic field does no work when a particle is displaced because the force is perpendicular to the displacement.

Dr. Jie ZouPHY Magnetic force acting on a current-carrying conductor Magnetic force on a straight segment of current-carrying wire in a uniform magnetic field: F B = I L  B. L: a vector; direction along I; magnitude equals to L. Magnetic force on a curved current-carrying wire in a uniform magnetic field: Net magnetic force acting on any closed current loop in a uniform magnetic field: Straight wire Curved wire Closed current loop

Dr. Jie ZouPHY An example

Dr. Jie ZouPHY Quick Quiz Rank the wires according to the magnitude of the magnetic force exerted on them.

Dr. Jie ZouPHY Example 29.2 Force on a semicircular conductor A wire bent into a semicircle of radius R forms a closed circuit and carries a current I. The wire lies in the xy plane, and a uniform magnetic field is directed along the positive y axis. Find the magnetic force acting on the straight portion of the wire and on the curved portion.