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Biot-Savart and Ampere's Law Worksheet, Assignments of Physics

This worksheet from general physics iii course covers problems related to biot-savart and ampere's law, including deriving equations, calculating magnetic field vectors, and determining magnetic forces for various wire configurations. Problems involve straight wires, quarter circle wire arcs, and current loops.

Typology: Assignments

Pre 2010

Uploaded on 08/18/2009

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koofers-user-h9b 🇺🇸

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Phy213: General Physics III 11/29/2020
Chapter 29 Worksheet 1
Biot-Savart Law
1. A straight wire horizontal wire, L=0.3 m, has a 1.5 A current running through it.
a. Using the Biot-Savart Law, derive the equation for the magnetic field vector produced by the
wire at an arbitrary point P, below the wire and halfway between the ends.
b. Determine the magnitude and direction of the magnetic field vector at point P=0.1 m below
the wire.
c. Determine the magnitude and direction of the magnetic field produced by the wire at a point
0.01 m to the left of point P.
d. Determine the magnitude and direction of the magnetic field at point P for a wire of
“infinite” length.
i = 1.5 A
y = .10 m
. P
L/2 L/2
pf3
pf4
pf5

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Chapter 29 Worksheet 1 Biot-Savart Law

  1. A straight wire horizontal wire, L=0.3 m, has a 1.5 A current running through it. a. Using the Biot-Savart Law, derive the equation for the magnetic field vector produced by the wire at an arbitrary point P, below the wire and halfway between the ends. b. Determine the magnitude and direction of the magnetic field vector at point P=0.1 m below the wire. c. Determine the magnitude and direction of the magnetic field produced by the wire at a point 0.01 m to the left of point P. d. Determine the magnitude and direction of the magnetic field at point P for a wire of “infinite” length. i = 1.5 A y = .10 m

L/2^.^ P

L/

Chapter 29 Worksheet 2

  1. A quarter circle wire arc (90o), with radius of curvature R=0.1 m, has a 2.0 A current running through it. a. Using the Biot-Savart Law, determine the equation for magnetic field vector produced by the arc at point P, located at the center of curvature. b. Calculate the magnetic field vector produced by the arc at point P. c. Derive the magnetic field vector at the center of a circular loop, of radius R. d. Determine the magnitude and direction of the magnetic field at the center of a circular loop, where R=0.1 m.
  2. Consider the current loop shown below, consisting of 2 concentric 90o^ arc segments of radii, R 1 and R 2 , connected by 2 segments that are parallel to the center of curvature for the arcs. The current flowing through the loop is 1.0 A, counter- clockwise. a. Using the Biot-Savart Law, determine the equations for the magnetic field vectors produced by each segment of the loop arc at point P, located at the center of curvature for both arc segments. b. Calculate the total magnetic field vector at point P, where R 1 =0.1 m and R 2 = 0.15 m. c. Determine the net magnetic force vector exerted on the outer arc segment of the loop due to the other segments.

. P

i = 1.0 A R 1 R 2

. P

R

i = 2.0 A . P

R

i = 2.0 A

Chapter 29 Worksheet 4

  1. Two infinitely long horizontal wires separated by 0.01 m have a current running through them (in opposite directions). a. Using Ampere’s Law, determine the magnitude and direction of magnetic field produced by both wires at a point 1 m below the lowest wire. b. Determine the magnitude and direction of the magnetic field produced by both wires at a point halfway between the two wires in (b). c. What is the magnetic force vector exerted by wire 1 on wire 2? d. If the separation between the wires were 1 m, determine the magnitude and direction of magnetic field produced by both wires at a point 1 m below the lowest wire. e. The current in wire 2 is increased to 2A. What is the magnetic force vector exerted by wire 2 on wire 1? i 1 = 2 A d = 1.0 m r = 0.01 m i 2 = 1 A

Chapter 29 Worksheet 5

  1. Consider a current carrying coil (i=0.5 A, counter-clockwise as viewed looking down), where the number of coils is 20 and the radius is 5.0 cm. a. Calculate the magnitude of the magnetic moment for the coil. b. Derive the magnetic field B along the central axis (i.e. in the z direction) of the coil. c. What is the magnetic field at z=20 cm above the coil? d. What is the magnetic field vector at z=40 cm above the coil? e. What is the magnetic field vector at z=80 cm above the coil? f. At what z distance does the magnetic field become effectively independent of the radius, i.e. the magnetic field can be calculated to within 3% when the radius is ignored? x y z R i