Two identical circular loops of radius R, each carrying a steady current I,are placed parallel to the xy-plane with their centers separated by a distanced.1. Derive an expression for the magnetic field produced by one loop atthe center of the other loop.2. Calculate the force exerted by one loop on the other due to their mutualmagnetic interaction.3. Discuss the sign of the force (attractive or repulsive) and how it dependson the direction of the currents in the loops.RLoop 2dLoop 1

Answered: Image /qna-images/answer/92dfe25e-320d-4388-aecb-b1ff55a7b537.jpg

Answered: Two identical circular loops of radius…

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter11: Magnetic Forces And Fields

Section: Chapter Questions

Problem 110CP: A circular loop of wire of area 10 cm2 carries a current of 25 A. At a particular instant, the loop...

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A wire ismade into a circular shape of radius R and pivoted along a central support.The two ends of the sire are touching a banish that is connected to a &power source. The stricture is between the poles of a magnet such that we can assume there is a uniform magnetic field on the wire. In terms of a coordinate system with origin at the center ofthe ring, magneticfieldisBx=B0,By=Bz= 0. and the ring rotates about the z-axis. Find the torque on the ring siren it is not in the xz-plane.
A 0.50-kg copper sheet drops through a uniform horizontal magnetic field of 1.5 T, and it reaches a terminal velocity of 2.0 m's. (a) What is the net map,-, eh: force on the sheet after it reaches terminal velocity? (b) Describe the mechanism responsible for this force, (c) How much power is dissipated as Joule heating while the sheet moves at terminal velocity?
The accompanying figure shows two long, straight, horizontal wires that are parallel and a distance 2a apart. If both wires carry current I in the same direction, (a) what is the magnetic field at P1? (b) P2?
Acircularcoiofwireofradius5.Ocmhas2Otums and carries a current of 2.0 A. The coil lies in a magnetic field of magnitude 0.50 T that is directed parallel to the plane of the coil. (a) What is the magnetic dipole moment of the coil? (b) What is the torque on the coil?
Two long, straight wires are parallel and 25 cm apart. (a) If each wire carries a current of 50 A in the same direction, what is the magnetic force per meter exerted on each wire? (b) Does tire force pull the wires together or push them apart? (c) What happens if the currents flow in opposite directions?
Two long wires, one of which has a semicircular tend of radius R, are positioned as shown in the accompanying figure. If both wires carry a current I, how far apart must then parallel sections be so that the net magnetic field at P is zero? Does the current in the straight wire flow up or down?
(a) A 200Turn circular loop of radius 50.0 cm is vertical, with its axis on an east-west line. A current of 100 A circulates clockwise in the loop when viewed from the east. The Earth’s field here is due norm, parallel to me ground, with a strength of 3.00105T. What are 1he direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?
A long, straight wire of radius R caries a current I that is distributed uniformly over the cross-section of the wire. At what distance from the axis of the wire is the magnitude of the magnetic field a maximum?
When the current through a circular loop is 6.0 A, the magnetic field at its center is 2.0104 T. What is the radius of the loop?
A uniform magnetic field of magnitude is directed parallel to the z-axis. A proton enters the field with a velocity v=(4j+3k)106m/s and travels in a helical path with a radius of 5.0 cm. (a) What is the value of B? (b) What is the time required for one trip around the helix? (c) Where is the proton 5.0107s after entering the field?
Unreasonable results A charged particle having mass 6.641027kg (that of a helium atom) moving at 8.70105m/s perpendicular to a 1.50-T magnetic field travels in a circular path of radius 16.0 mm. (a) What is the charge of the particle? (b) What is unreasonable about this result? (c) Which assumptions are responsible?
(a) A physicist performing a sensitive measurement wants to limit the magnetic force on a moving charge in her equipment to less than 1.001012N. What is the greatest the charge can be if it moves at a maximum speed of 30.0 m/s in Earth's field? (b) Discuss whether it would be difficult to limit the charge to less than the value found in (a) by comparing it with typical static electricity' and noting that static is often absent,

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