 Phyllis Fleming Physics Physics 108
 Review - Magnetic Fields
 1 Given that the magnetic force Fm on a positively charged particle with charge q traveling with a velocity v in a magnetic field B is Fm = q(v x B), where the unit of B is Tesla (T), find the Tesla in terms of the following units: N, C, m, and s or N, A, and m.
 2 The magnetic force Fm on a charge q moving with a velocity v in a magnetic field B is given by Fm = q(v x B). Which of the following statements are always true? (a) Fm is always perpendicular to v. (b) v is always perpendicular to B. (c) Fm is always perpendicular to B.
 3 A uniform magnetic field B, with magnitude B = 1.2 x 10-3 T, points vertically upward throughout the volume of a laboratory chamber. A proton with a velocity v = 3.2 x 107 m/s enters the laboratory moving horizontally from south to north. Find (a) the magnitude and (b) the direction of magnetic force on the proton.
 4 A proton moves in a uniform magnetic field B with a speed of 107 m/s and experiences an acceleration of 2 x 1013 m/s2 in the +X-direction when its velocity is in the +Z-direction. Determine the magnitude and direction of the magnetic field for which the magnitude of the field is a minimum.
 5 An electron moves with a speed v = 2 x 107 m/s through a magnetic field of B = 0.080 N-s/C-m. (a) What are the greatest and smallest forces the magnetic field may exert on the electron? (b) If the acceleration of the electron is 1.41 x 1017 m/s2, what angle does the velocity make with the magnetic field? The electron has a mass m = 9.1 x 10-31 kg and its charge e = 1.6 x 10-19 C.
 6 A particle of charge q = 10-6 C moves to the right with velocity v = 103 m/s in a magnetic field B = 2 N-s/C-m which makes an angle of 30o with v. Find the magnitude of the force on the charged particle.
 7 An electron moving with velocity v enters a constant magnetic field. What will its path through the field look like if it enters (a) parallel to the field direction? (b) perpendicular to the field direction? (c) at some other angle to the field direction? (d) In which of the above cases will the electron be accelerated?
 8 Two charged particles with the same mass and charge q move in circular paths in a magnetic field B that is perpendicular to their velocities. If particle A has a velocity vA and particle B has a velocity vB, compare the time for the particles to make one complete orbit.
 9 Single ionized neon atoms (neon atoms that have lost one electron) enter a uniform magnetic field B. All of the atoms have the same velocity v, which is perpendicular to B. The radius of the circular path of the atoms with mass m1 is 20 cm and for those with mass m2 it is 22 cm. What is the ratio of m2 to m1?
 10 In a space laboratory, an object of mass m = 10-3 kg and charge q = 2 x 10-5 C moves in a circular orbit of radius r = 102 m about a fixed charge Q = -10-4 C. There is a uniform magnetic field B = 4 N-s/C-m down into the plane of the orbit. Find (a) the magnitude and direction of the electric force acting on the object of mass m, (b) the magnetic force on the object in terms of its velocity v, (c) the direction of the magnetic force if (i) the object moves in a clockwise direction as you look down at the orbit and (ii) if the object moves in the opposite direction. (d) Use Newton's second law of motion to determine for what velocity v the object will move in a circle of radius 102 m. Your solution will lead you to a quadratic equation. Your knowledge of physics will allow you to interpret the solutions.
 11 A particle with a mass m = 2.0 x 10-12 kg velocity v = 106 m/s and charge q = 10-6 C enters region 1 between the parallel plates where there is an electric field E = 106 N/C. Find (a) the direction and magnitude of the magnetic field B perpendicular to the velocity of the particle in Region 1 that allows the particle to pass through Region 1 without a deflection, (b) the direction of the deflection of the particle with B as found in (a) if its velocity is (i) 5 x 105 m/s and (ii) 5 x 106 m/s. The particle now enters Region 2 where there is no electric field, but a magnetic field B’ = 2.0 T perpendicular to v. The magnitude of v is again 106 m/s. (c) What is the direction of B’ to make the particle go in a counterclockwise circular path? (d) What is the radius of the circle? 12 In a certain region of space there is a magnetic field B, but no electric field. A particle of charge +10-6 C, moving to the right at v1 = 500 m/s, experiences a force F1, directed out of the paper, of magnitude 3.0 x 10-3 N (Fig. 2a below). The same particle moving into the paper at v2 = 500 m/s experiences a force F2 in the plane of the paper (Fig. 2b below). Find (a) the magnitude and direction of B. (b) the magnitude of F2 and (c) the magnitude and direction of F3 on the particle if it moves with velocity v3 = 103 m/s as shown in Fig. 2c below. (d) If the particle has mass m = 10-8 kg, where is the center of the circular orbit for the velocity in Fig. 2b? For this figure describe the plane in which it moves. 13 Two smooth conducting rails a distance L = 2.0 m apart make an angle of 22.5o with the horizontal. A bar of mass 1.2-kg rests across the rails, as shown in Fig. 3 below. There is a uniform magnetic field vertically upward equal to 0.50 N-s/C-m. A battery is connected to cause a current I to flow through the bar as shown. (a) Draw a side view of the bar and indicate the cause and direction of each force that acts on it. There is no friction, but do not forget gravity. (b) What current I will allow the bar to remain at rest? 14 A wire carrying a current is in a north-south direction. The north-seeking pole of a compass needle placed above the wire is deflected toward the west. What is the direction of the current in the wire?
 15 Figure 4 below represents a wire carrying a current into the page. Sketch a magnetic field line due to the current-carrying wire. What is the direction of the magnetic field at P1?  at P2? 16 The magnetic field B due to a very long wire carrying a current I at a distance r from the wire is 0.50 T.  Find the magnetic field due to the long wire if (a) I is doubled and r is halved or (b) I is halved and r is doubled.
 17 Figure 5 below represents two wires carrying currents into the page. (a) What is the magnitude of the magnetic field at point P1, which is halfway between the wires, if both wires carry current I. (b) What is the direction and magnitude of the magnetic field at P2. (c) If a proton moves out of the paper at P2 parallel to the current-carrying wires, what is the direction of the force exerted on it? 18 Two very long wires carrying a current I of 3.0 A out of the page are at two of the corners of an equilateral triangle, as shown in Fig. 6 below. The sides of the triangle are 1.0 m long. Find the direction and magnitude of the magnetic field at P, the third corner of the triangle. 19 Two parallel wires carrying current in the same direction attract each other. Describe this experimental result as an interaction between the field due to one wire and the motion of charges in the other wire.
 20 In Fig. 7 below, the very long straight wire carries a current I = 10 A and the rectangular loop carries a current I’= 20 A. Find the magnitude and direction of the force on the loop.  a = 0.01 m,  b = 0.03 m, and L = 0.03 m. 21 The rectangular loop of Fig. 8 has a length of 0.25 m and width of 0.20 m. It is hinged along the y-axis and rotates about this axis. The plane of the coil makes an angle of 30o with the X-axis. The coil carries a current I = 1.0 A and is in a magnetic field B = 0.5 N/A-m.  Find the torque on the loop. 22 If the current in a circular loop is in a counterclockwise direction as you view it, what is the direction of the magnetic field due to the current carrying loop along its axis?
 23 An electron travels with a velocity v along the axis of a current-carrying loop. What will happen to the electron?
 24 A long solenoid with 1000 turns per meter carries a current of 0.20 A.  As viewed from the right end of the solenoid, the current in the coils of the solenoid is counterclockwise. (a) Find the direction and magnitude of the magnetic field due to the solenoid. A current of 6.0 A exists in a long straight wire along the axis of the solenoid, with the direction of the current to the left. (b) Find at what radial distance the direction of the resultant magnetic field due to the solenoid and the long straight wire is at an angle of 45o to the axial direction of the solenoid.
 25 I describe a toroid as a solenoid bent into the shape of a doughnut. For a toroid with inner radius a and outer radius b, find the magnetic field of the toroid, which carries a current  I,  for (a) r ≤ a,  (b) a ≤ r ≤ b, and (c) r ≥ b.
 26 In the review for electric fields, I commented that there were two problems related to electric fields: (a) given a distribution of charges, find the electric field due to them and (b) given an electric field, find the force on a charge particle q in this field.  Please do a similar analysis for magnetic fields.
 27 A thin, straight, rigid wire coincides with the X-axis with the left end at the origin 0 and the other end at C. A steady current of 6.0 A is directed from 0 to C. The other end of the wire is at x = 0.5 m. Over the entire length OC, there is a magnetic field B directed along the Y-axis. The magnitude of the field B = (1 T + 3x2 T/m2). Find (a) the magnitude of the force dF exerted on the current element I dx, (b) the units and direction of dF, (c) the magnitude of the torque dτ exerted on the element dx about the Y-axis, (d) the magnitude of the torque dτ exerted on the element dx about the Z-axis and (e) the force on the entire length OC due to the magnetic field B. 28 A steady current I is maintained in the conducting path ACDE of Fig. 10 below. Find the magnetic field at P located at the center of the circular arc CD of radius R subtending an angle of 150o.  What is the direction of B? 29 Bending a very long wire as shown in Fig. 11 forms a long hairpin. If the wire carries a current I, what is the magnitude and direction of the magnetic field at point P. Your answer will be in term of symbols. The radius of the loop at the left end is very small compared to the lengths of the straight sections of the wire. 30 In the coaxial arrangement of Fig. 12 below, a current I in the inner cylinder of radius a is out of the page and a current I in the outer cylindrical shell of inner radius b and outer radius c is into the page. Find the magnetic field (direction and magnitude) for (a) r ≤ a, (b) a ≤ r ≤ b, (c) b ≤ r ≤ c, and (d) r ≥ c. 31 Figure 13 below shows a cross-sectional view of a large number N of long, thin, straight wires which are closely spaced in the X-Y plane, forming a single layer w in width. Each wire is parallel to the Y-axis and carries a current I out of the X-Y plane (i.e., the plane of the paper). (a) Starting with the expression B = µoI/2 πr that represents the magnetic field due to an infinitely long, slender wire, write an expression for dB, the contribution to the magnetic field at P due to the current in an element of width dx located at a distance x from the origin. The point P is located on the Z-axis a distance a from the X-Y plane and is equidistant from the edges of the layer. (b) Calculate B due to the current in the entire layer of width w. 32 You found that the magnetic field B of a circular loop of radius R carrying a current I at a point P on the axis of the loop a distance z from the center of the loop is given by B = µoI πR2/2 π(R2 + z2)3/2.  (a) What does the magnetic moment µ of the loop equal? (b) Rewrite B in terms of the magnetic moment µ of the loop. (c) Find the expression for B from Part (b) when z is much greater than R.  (d) Find the magnetic field due to a spinning electron with magnetic moment µ = 9.27 x 10-24 A-m2 at P a distance z = 10-10 m.  A second spinning electron is at P on the axis of spin of the first one. (e) Find the potential energy (in electron volts) of the magnetic moment of the second electron in the magnetic field of the first spinning electron if the two electron spins are (i) parallel and (ii) antiparallel.  Which orientation has the least energy?

 Homepage Sitemap
 Website Designed By: Questions, Comments To: Date Created: Date Last Updated: Susan D. Kunk Phyllis J. Fleming August 8, 2002 April 30, 2003