Fall 2012

Physics 121 Practice Problem Solutions 09 Magnetic Fields

Contents:

121P09 - 4P, 9P, 16P, 35P*, 38P, 40P, 57P, 59P

• Overview• What Produces Magnetic Field • The Definition of B. Force on a moving Charge• Crossed Fields: Discovery of the Electron• A Charged Particle Circulating in a Magnetic Field –

Cyclotron Frequency• The Mass Spectrometer and Cyclotron• Magnetic Force on a Current-Carrying Wire• Torque on a Current Loop• The Magnetic Dipole Moment• Crossed Fields: The Hall Effect (Optional Sect. 28.5)

Fall 2012

PROBLEM 121P09-4P*: An electron that has velocity

moves through the magnetic field B = (0.030 T)i - (0.15 T)j . (a) Find the force on the electron. (b) Repeat your calculation for a proton having the same velocity.

Fall 2012

PROBLEM 121P09-9P*: An electron is accelerated through a potential difference of 1.0 kV and directed into a region between two parallel plates separated by 20 mm with a potential difference of 100 V between them. The electron is moving perpendicular to the electric field of the plates when it enters the region between the plates. What uniform magnetic field, applied perpendicular to both the electron path and the electric field, will allow the electron to travel in a straight line?

Fall 2012

PROBLEM 121P09-16P: An electron is accelerated from rest by a potential difference of 350 V. It then enters a uniform magnetic field of magnitude 200 mT with its velocity perpendicular to the field. Calculate (a) the speed of the electron and (b) the radius of its path in the magnetic field.

Fall 2012

PROBLEM 121P09-35P*: A wire of 62.0 cm length and 13.0 g mass is suspended by a pair of flexible leads in a uniform magnetic field of magnitude 0.440 T (See figure ). What are the magnitude and direction of the current required to remove the tension in the supporting leads?

Fall 2012

PROBLEM 121P09-38P: Consider the possibility of a new design for an electric train. The engine is driven by the force on a conducting axle due to the vertical component of Earth's magnetic field. To produce the force, current is maintained down one rail, through a conducting wheel, through the axle, through another conducting wheel, and then back to the source via the other rail. (a) What current is needed to provide a modest 10 kN force? Take the vertical component of

Earth's field to be 10 µµµµT and the length of the axle to be 3.0 m. (b) At what rate would electric energy be lost for each ohm of resistance in the rails? (c) Is such a train totally or just marginally unrealistic?

Fall 2012

PROBLEM 121P09-40P: A single-turn current loop, carrying a current of 4.00 A, is in the shape of a right triangle with sides 50.0, 120, and 130 cm. The loop is in a uniform magnetic field of magnitude 75.0 mT whose direction is parallel to the current in the 130 cm side of the loop. (a) Find the magnitude of the magnetic force on each of the three sides of the loop. (b) Show that thetotal magnetic force on the loop is zero.

Fall 2012

Problem 121P09 – 40 page 2

Fall 2012

Problem 121P09 – 40 page 3

Fall 2012

Problem 121P09 – 40 page 4

Fall 2012

PROBLEM 121P09-57P: A proton moves at a constant velocity of +50 m/s along an x axis, through

crossed electric and magnetic fields. The magnetic field is B = (2.0 mT) . What is the electric field?

Fall 2012

PROBLEM 121P09-59P: An electron moves through a uniform magnetic field given by B = Bx

i + (3B

x) j . At a particular instant, the electron has the velocity v = (2.0 i + 4.0 j ) m/s and the magnetic

force acting on it is (6.4 x10-19 N) k . Find Bx.