Ch 26: Magnetic Fields and ForcesSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Circular Motion of Charges in Magnetic Fields

Practice: A 4 kg, 3 C (unknown sign) charge originally moving in the +x axis with 5 m/s when it enters (red arrow) a small square area that has a constant magnetic field, as shown below. The field causes the charge to be deflected, and it exits the area moving in the +y axis. What is the magnitude of the magnetic field? (Is this charge +3 C or – 3 C?)

Additional Problems
A charged particle of mass 0.0070 kg is subjected to a 5.0 T magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius 0.10 m at a speed of 5.0 m/s, what is the magnitude of the charge on the particle? A) 0.070 C B) 1400 C C) 14 C D) 0.00070 C
A positive charge q = 1.60 x 10 -19 C moves in a horizontal circle with a speed v = 3.65 x 107 m/s in a homogeneous and perpendicular magnetic field of 1.20 Tesla as shown. Calculate the centripetal force F on the charge. 
A small sphere with positive charge q = 5.00 x 10 -4 C and mass 2.00 x 10 -5 kg is moving in a region of uniform magnetic field. The object moves counterclockwise in a path that is a horizontal circle with radius R = 0.0080 m, as shown in the sketch. The speed of the sphere is a constant 3.0 m/s. Gravity can be neglected. What are the magnitude and direction of the magnetic field in the region? Write the direction in blank provided and also show the direction in the sketch. (Note: The acceleration for uniform circular motion is arad = v2/R.) Ans. B =  direction = 
In the figure, a uniform magnetic field points into the page. (The magnetic field vectors are indicated by ⊗ symbols.). Four particles with the same mass follow the paths shown as they pass through the magnetic field with identical, constant speeds. What can we conclude about the charge on each particle? (Discuss sign, and relative magnitudes.)
Two regions in space, Region 1 and Region 2, are separated by a gap of thickness  d filled with a magnetic field of B pointing into the page, as shown in the figure.  If d = 1 cm and B = 0.1 T, what is the minimum kinetic energy required for an electron to penetrate from Region 1 into Region 2? (1) 1.4 × 10−14 J (2) 2.8 × 10−14 J (3) 2.1 × 10−14 J (4) 3.5 × 10−14 J (5) 4.2 × 10−14 J
A static uniform magnetic field is directed into the page. A charged particle moves in the plane of the page following a counterclockwise spiral of decreasing radius as shown. Neglect the effect due to gravity. What is a reasonable explanation? 1. The charge is neutral and speeding up. 2. The charge is positive and with a constant speed. 3. None of these 4. The charge is neutral and with a constant speed. 5. The charge is negative and with a constant speed. 6. The charge is positive and slowing down. 7. The charge is negative and slowing down. 8. The charge is neutral and slowing down. 9. The charge is positive and speeding up. 10. The charge is negative and speeding up.
Consider the circular motion of a positively charged particle in the plane of this paper, due to a constant magnetic field B which points out of the paper. Neglect the effect due to gravity. What is the direction of the orbital motion of the particle? Suppose the tangential speed of the charged particle is increased to twice the original tangential speed. (vnew = 2 vold). B is fixed. What is the ratio of the new frequency to the old frequency? Note: Unit for frequency is the number of revolutions per unit time. 1. fnew / fold = 1/3 2. fnew / fold = 2 3. fnew / fold = 1 4. fnew / fold = 3 5. fnew / fold = 1/4 6. fnew / fold = 1/2 7. fnew / fold = 4