LECTURE 22 MAGNETIC TORQUE & MAGNETIC FIELDS. Instructor: Kazumi Tolich

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1 LECTURE 22 MAGNETIC TORQUE & MAGNETIC FIELDS Instructor: Kazumi Tolich

2 Lecture 22 2! Reading chapter 22.5 to 22.7! Magnetic torque on current loops! Magnetic field due to current! Ampere s law! Current loops and solenoid

3 Quiz: 1 3! As shown, current is flowing counterclockwise in a square loop that is placed in a uniform magnetic field directed out of the page. Is there a net magnetic force on the loop? If so, in which direction? A. No. The net force is zero. B. Yes. To the left. C. Yes. To the right. D. Yes. Up. E. Yes. Down. F. Yes. Out of the page. G. Yes. Into the page.

4 Quiz: 22-1 answer 4! No. The net force is zero.! Since the same amount of current flows in each of the four wire segments, the magnitude of the magnetic force on each segment is the same:! = #$% sin ) = #$%.! Using the right-hand rule, we find that each of the four wire segments will experience a force outward from the center of the loop.! Thus, the forces of the opposing segments cancel, so the net force is zero.! Net force on a current carrying loop in a uniform magnetic field is always zero.! Follow-up: Does this loop rotate?

5 Quiz: 2 5! As shown, current is flowing clockwise in a square loop that is placed in a uniform magnetic field directed to the left. Does the loop rotate? If so, in which direction would the loop rotate at the moment shown? A. No. B. Yes. It will rotate about the vertical axis with the right segment moving out of the page. C. Yes. It will rotate about the vertical axis with the left segment moving out of the page. D. Yes. It will rotate about the horizontal axis with the top segment moving out of the page. E. Yes. It will rotate about the horizontal axis with the bottom segment moving out of the page. F. Yes. It will rotate clockwise. G. Yes, it will rotate counterclockwise.

6 Quiz: 22-2 answer 6! Yes. It will rotate about the vertical axis with the left segment moving out of the page.! Apply the right hand rule.! The force on the right segment is into the page.! The force on the left segment is out of the page.! The force on the top and bottom segments are zero.

7 Torque on a loop 7! The magnetic torque on a current carrying loop with an area * and + turns is given by, = +#*% sin )! We will see in the future lecture that electric motors work using this torque.

8 Example: 1 8! A single circular loop of radius r = 0.23 m carries a current of I = 2.6 A in a uniform magnetic field of B = 0.95 T. a) What is the maximum torque exerted on this loop? b) Find the angle the plane of the loop must make with the field if the torque is to be half its maximum value.

9 Magnetic field due to current 9! Electric current can create magnetic fields that form circles around the current.! The magnetic field is always perpendicular to the direction of the current that creates it.! The magnitude of the magnetic field around a long, straight wire is given by % = -.# 201

10 Ampere s law 10! Ampere s law relates the constant current through a surface defined by a closed path (Amperian loop) to the magnetic field along the path: 2 % $ = -. # 6789:;6<! where -. = 40> >10 BC T E m A is the permeability of free space.

11 Quiz: 3 11! Consider the long, straight, current-carrying wires shown. One wire carries a current of # I in the positive J direction; the other wire carries a current of # K in the positive L direction (# I = # K ). Rank the magnetic field at the two points, A or B. M M M M # I # K

Quiz: 22-3 answer 12!! B<A If there are multiple sources of magnetic field, the magnetic field at a particular location is the vector sum of magnetic fields due to each source.

12 Quiz: 22-3 answer 12!! B<A If there are multiple sources of magnetic field, the magnetic field at a particular location is the vector sum of magnetic fields due to each source.! The direction of the magnetic field can be found by the right hand rule.! #I produces magnetic field pointing out of the page at A, and into the page at B.! #K produces magnetic field pointing out of the page at A and B.! The magnitudes of the magnetic field produced by #I or #K alone is the same at A and B since N P %= O. KQR! Follow-up: What is the net magnetic field at B? M M M M #I #K

13 Example: 2 (Walker 22-48) 13! Consider the long, straight, current-carrying wires shown. One wire carries a current of 6.2 A in the positive J direction; the other wire carries a current of 4.5 A in the positive L direction. Calculate the magnitude of the net magnetic field at point A and B.

14 Quiz: 4 14! Two wires lying in the plane of this page carry currents in opposite directions, as shown. Do these wires exert force on each other? A. Yes. The bottom wire will repel the top wire, but the top wire will attract the bottom wire. B. Yes. The top wire will repel the bottom wire, but the bottom wire will attract the top wire. C. Yes. They are attracted to each other. D. Yes. They repel each other. E. No.

15 Quiz: 22-4 answer/demo: 1 15! Yes. They repel each other.! Parallel hanging wires are either attracted or repelled by one another, depending on the directions of current in the wires.! The magnitude of the force is given by d! = -.# I # K 20M

16 Circular current loop 16! The magnetic field of a current loop is similar to the magnetic field of a bar magnet. At the center of the loop of radius S, + turns, carrying a current #, the magnetic field is given by % = +-.# 2S

17 Solenoid 17! A solenoid is a helix of closely spaced turns. The magnetic field inside a long solenoid is parallel to its axis. % = -. T#! T is the number of turns per unit length. MRI

18 Demo: 2 18! Magnetic fields around conductors! Visualizing magnetic field using iron filings! Electromagnet! A small electromagnet powered by a 1.5V battery that can hold several kilograms.! A huge coil carries up to 25A; very strong field will attract nails, etc. that are thrown near.

19 Electric bells 19! When a current is applied, B field is created, which attracts the clapper to the electromagnet.! This breaks the circuit, collapsing the B field of the electromagnet. Electromagnet Switch Clapper

21 MAGNETIC FORCES AND MAGNETIC FIELDS

21 MAGNETIC FORCES AND MAGNETIC FIELDS CHAPTER 1 MAGNETIC FORCES AND MAGNETIC FIELDS ANSWERS TO FOCUS ON CONCEPTS QUESTIONS 1 (d) Right-Hand Rule No 1 gives the direction of the magnetic force as x for both drawings A and B In drawing C, the