Electric and Magnetic Forces on Charges and Current-Carrying Wires - Prof. Xiangjun Xing, Assignments of Physics

Download Electric and Magnetic Forces on Charges and Current-Carrying Wires - Prof. Xiangjun Xing and more Assignments Physics in PDF only on Docsity! 33.61. Model: Electric and magnetic fields exert forces on a moving charge. The fields are uniform throughout the region. Visualize: Please refer to Figure P33.61. Solve: (a) We will first find the net force on the antiproton, and then find the net acceleration using Newton’s second law. The magnitudes of the electric and magnetic forces are ( )( ) ( )( )( ) 19 16 E 19 16 B 1.60 10 C 1000 V/m 1.60 10 N 1.60 10 C 500 m/s 2.5 T 2.00 10 N F eE F evB − − − − = = × = × = = × = × The directions of these two forces on the antiproton are opposite. EF points up whereas, using the right-hand rule, BF points down. Hence, ( )16 16net 2.0 10 N 1.60 10 N, downF − −= × − × 16net 0.40 10 NF ma−⇒ = × = ⇒ 16 10 2 27 0.40 10 N 2.4 10 m/s , down 1.67 10 kg a − − ⎛ ⎞× = = ×⎜ ⎟×⎝ ⎠ (b) If v were reversed, both EF and BF will point up. Thus, ( )16 16net 1.6 10 N 2.0 10 N, upF − −= × + × ⇒ 16 11 2 27 3.6 10 N 2.2 10 m/s , up 1.67 10 kg a − − ⎛ ⎞× = = ×⎜ ⎟×⎝ ⎠ 33.67. Model: A magnetic field exerts a magnetic force on a length of current-carrying wire. We ignore gravitational effects, and focus on the B effects. Visualize: Please refer to Figure P33.67. The figure shows a wire in a magnetic field that is directed out of the page. The magnetic force on the wire is therefore to the right and will stretch the springs. Solve: In static equilibrium, the sum of the forces on the wire is zero: FB + Fsp 1 + Fsp 2 = 0 N ⇒ ILB + (−kΔx) + (−kΔx) ⇒ ( )( ) ( )( ) 2 10 N/m 0.01 m2 2.0 A 0.20 m 0.5 T k xI LB Δ = = =