Ch 27: Sources of Magnetic FieldWorksheetSee 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
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Ch 10: Rotational Kinematics
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Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
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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: Ampere's Law with Calculus

Example #1: Magnetic Field Inside a Solenoid

Practice: A solid, cylindrical conductor carries a uniform current density, J. If the radius of the cylindrical conductor is R, what is the magnetic field at a distance 𝒓 from the center of the conductor when r < R? What about when r > R?

Additional Problems
A hollow cylindrical conductor (inner radius = a, outer radius = b) carries a current I uniformly spread over its cross section. Which graph below correctly gives the magnetic field as a function of the distance r from the center of the cylinder?
A coaxial cable has two components: a thin wire at its center, carrying a current "forward", and a thin cylindrical shell surrounding the wire, carrying a current "backwards", with each current being the same magnitude. If the magnitude of the current was 1 A, and the cylindrical shell had a radius of 2 cm,  what is the magnitude of the magnetic field at (a) some distance r &lt; 2 cm from the inner wire and (b) some distance r &gt; 2 cm from the inner wire?
A solid, cylinderical conductor of radius 1.5 cm carries a current density of 14 A/m 2. What is the magnetic field of this conductor at its surface?
Consider the toroid shown in the figure (inner radius 5cm, outer radius 10cm). What is the magnitude of the magnetic field inside a toroid of 1200 turns carrying a current 0.8 A at a distance 7cm from the center of the toroid? (Hint: Use Ampere's Law applied to a closed loop in the toroid mid-plane, as shown by a dash line) A) 2.74 mT B) 1.67 mT C) 3.33 mT D) 4.92 mT E) 0.83 mT
A solid, cylinderical conductor of radius 1.5 cm carries a current density of 14 A/m 2. What is the magnetic field of this conductor at its surface?
Consider N parallel wires, each carrying a current i. If an Amperian loop was chosen that enclosed some of the wires, which of the following statements is true: (a) The line integral ∫ Bdl would be independent of the number of wires enclosed (b) The line integral ∫ Bdl would be independent of the radius of the Amperian loop (for a given number of wires enclosed) (c) Halving the number of wires enclosed would reduce the line integral ∫ Bdl by 1/4 (d) The line integral ∫ Bdl is independent of the current in each wire i, only depending on the number of wires enclosed