.Important Information:
m(proton) = 1.67 x 10^-27 kg; m(electron) = 9.11 x 10^-31 kg

1. A proton falls from rest through a potential difference, acquiring a speed of 8.0 x 10⁶ ms^-1. It then enters a region perpendicular to a 0.50 T magnetic field. How large is the radius of the circle in which the proton travels in a counterclockwise direction in the plane of the paper? What is the direction of the magnetic force? Ans: ; 0.17 m; - z
2. An electric power line carries a current of 1400 A in a location where the earth’s magnetic field is 5.0 x 10^-5 T. The line makes an angle of 75° with respect to the field. Determine the magnetic force on a 120 m length of wire. Ans: 8.1 N
3. A proton enters 1.5 T field with a velocity of 2.0 x 10⁷ ms^-1 at an angle of 30° with the field. What is the force on the proton? Ans: 2.4 x 10^-12 N
4. A proton moving at 5.0 x 10⁶ m/s enters a 0.40 T field directed at 30°. What is the magnitude and direction of the proton’s acceleration? What would its magnitude and direction be if it were an electron? Ans: 9.6 x 10¹³ ms^{- 2}, up; 1.8 x 10¹⁷ ms^{- 2}, up
5. An electron in a vacuum is first accelerated by a voltage of 11,000 V and then enters a region in which there is a uniform magnetic field of 0.100 T at right angles to the direction of the electron’s motion. The electron’s speed when it enters the field is 6.22 x 10⁷ ms^-1. What is the force on the electron due to the magnetic field? Ans: 9.95 x 10^-13 N
6. A proton in a cyclotron is moving with a speed of 2.00 x 10⁷ ms^-1 in a circle of radius 0.500 m. What force is exerted on the proton by the cyclotron? What is the magnitude of the magnetic field necessary to keep it moving in this circle? Ans: 1.34 x 10^-12 N; 0.42 T
7. A square, single-turned coil 0.20 m on a side is placed with its plane perpendicular to a constant magnetic field. An emf of 18 mV is induced when the coil moves through the field at a speed of 10 cms^-1. What is the magnitude of the magnetic field? Ans: 0.90 T
8. The sliding bar has a length of 0.50 m and moves at 2.0 ms^-1 in a magnetic field of 0.25 T. Find the induced voltage in the moving rod. If the resistance in the circuit is 0.50 ohms, find the current in the circuit. Ans: 0.25 V; 0.50 A
9. Two antiparalllel currents flow in a pair of horizontal wires separated by 20 cm. The upper horizontal wire carries a 20 A current from right to left. The lower horizontal wire carries a 30 A current from left to right. Calculate the magnitude and determine the direction of the net magnetic field at a point 5 cm above the lower wire. Calculate the magnitude and determine the direction of the net magnetic field at a point 5 cm above the upper wire. Ans: 1.5 x 10^-4 T, +z; 5.6 x 10^-5 T, -z

Magnetostatics Notes

Magnetostatics Hand Rule Class Problems