Ch 27: Sources of Magnetic FieldWorksheetSee all chapters
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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
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Ch 22: Electric Force & Field; Gauss' Law
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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: Magnetic Field Produced by Loops and Solenoids

Example #1: Find How Many Loops in a Solenoid

Practice: The single loop below has a radius of 10 cm and is perpendicular to the page (shown at a slight angle so you can better visualize it). If the magnetic field at the center is 10-6 T directed left, what is the magnitude of the current? What is the direction of the current at the top of the wire: into the page (towards left) or out of the page (towards right)?

Example #2: Designing a Solenoid (Total Length of Wire)

Practice: A long wire having total resistance of 10 Ω is made into a solenoid with 20 turns of wire per centimeter. The wire is connected to a battery, which provides a current in order to produce a 0.04 T magnetic field through the center of the solenoid. What voltage must this battery have?

Example #3: Find Magnetic Field By Two Concentric Loops

Practice: The two tightly wound solenoids below both have length 40 cm and current 5 A in the directions shown. The left solenoid has radius 20 cm and 50 m of total wire. The right solenoid has radius 0.5 cm and 314 m of total wire. The thinner solenoid is placed entirely inside the wider one so their central axes perfectly overlap. Assume wires don’t touch. What is the magnitude and direction of the magnetic field that is produced by a combination of the two solenoids at their central axis?

Additional Problems
A solenoid of 200 turns carrying a current of 2 A has a length of 25 cm. What is the magnitude of the magnetic field at the center of the solenoid? A) 5 mT B) 3 mT C) 2 mT D) 4 mT
Two round concentric metal wires lie on a tabletop, one inside the other. The inner wire has a diameter of 20.0 cm and carries a clockwise current of 12.0 A, as viewed from above, and the outer wire has a diameter of 30.0 cm. What must be the magnitude and direction (as viewed from above) of the current in the outer wire so that the net magnetic field due to this combination of wires is zero at the comment center of the wires?
A long, straight wire carries a current of I 1 = 8.0 A. A circular loop of wire lies immediately to the right of the straight wire, with the plane of the loop parallel to the wire. The loop has a radius of R = 0.03 m and carries a current of I2 = 2.0 A. Assuming that the thickness of the wires is negligible, find the magnitude and direction of the net magnetic field at the center of the loop.
Point P is at the center of a circular loop of wire. Current  I travels around the loop in a clockwise direction, as shown in the sketch. The magnetic field at point P is  A) zero B) into the page C) out of the page D) to the left E) to the right F) toward the top of the page G) toward the bottom of the page
A circular current loop lies in the x-z plane. What is the direction of the magnetic field outside of the loop in the x-z plane? A. the positive x-direction. B. the negative x-direction. C. the positive y-direction. D. the negative y-direction. E. depends on which part of the loop you are looking at.
A circular coil with 50 turns and a radius of 2 cm lies at the center of a larger coil with 100 turns and a radius of 5 cm. While the center of each loop coincides, the smaller loop's surface is rotated 30° away from the surface of the larger loop, as shown in the figure (from a top-down perspective). If the larger loop carries a current of 10 A, and the smaller loop carries a current of 15 A in the same direction, what is the magnitude of the magnetic field at the center of the loops?
A large MRI magnet is a large solenoid (with superconducting wires having zero resistance) with diameter 0.60 m and length 1.8 m. During normal operation, the current through the windings is 110 A and the magnetic field magnitude is 1.3 T. How many total windings does the MRI magnet have? (1) 16,900 (2) 9,400 (3) 13,000 (4) 15,500 (5) 14,700
Consider a solenoid that is very long compared to the radius. Of the following choices, the most effective way to increase the magnetic field in the interior of the solenoid is to do which of the following? A) overwrap the entire solenoid with an additional layer of current-carrying wire B) double its length, keeping the number of turns per unit length constant C) reduce its radius by half, keeping the number of turns per unit length constant D) replace the wire by a superconducting material
A wire carrying a current is shaped in the form of a circular loop of radius 4.0 mm. If the magnetic field strength at its center is 1.1 mT with no external magnetic fields contributing to it, what is the magnitude of the current that flows through the wire? A) 14 A B) 22 A C) 17 A D) 7.0 A
A wire in which there is a current of 3.09 A is to be formed into a circular loop of one turn. If the required value of the magnetic field at the center of the loop is 9.6 μT, what is the required radius? The permeability of free space is 1.25664 × 10−6 T · m/A. 1. 30.0092 2. 20.224 3. 29.2932 4. 50.2501 5. 32.3643 6. 42.8843 7. 55.4991 8. 19.6611 9. 16.7263 10. 33.25
A long straight wire carries current  I1 = 16.0 A and a circular loop of wire with radius  r = 0.200 m carries current I2 = 22.0 A. The two currents are in the directions shown in the sketch. The edge of the loop is 0.0500 m from the wire. What are the magnitude and direction of the resultant magnetic field at point P, which is at the center of the loop?
A solenoid 3.0 cm long consists of 6658 loops of wire. If the magnetic field inside the solenoid is 2.0 T, what is the magnitude of the current that flows through it?A) 0.14 AB) 90 AC) 3.0 AD) 7.2 A