Forces on currents Physics 132: Lecture e 19 Elements of Physics II Agenda for Today Currents are moving charges Torque on current loop Torque on rotated loop Currents create B-fields Adding magnetic fields Force between wires Physics 201: Lecture 1, Pg 1
Currents Create B-Fields Magnitude: I B 0 I 2 r 0 4 10 7 Tm / A 7 B r Current I OUT r = distance from wire Direction of B-field from current carrying wire: Curly right hand rule Lines of B Thumb along current I, direction of B along curled fingers. Physics 201: Lecture 1, Pg 2
Clicker Question 9: A square loop of wire carries a current I. Current is flowing in a counterclockwise direction as shown. What is the direction of the magnetic field at A? (a) (b) (c) into the page out of the page the B-field is zero Physics 201: Lecture 1, Pg 3
B-Field Caused by a Looped Wire If we make a current carrying wire into a loop, what total B-field will it make? B-field points out of loop!! Bottom? Right side? Left side? Top? Total field??? Curly right hand rule Physics 201: Lecture 1, Pg 4
Magnetic Field of a Current Loop Total Field Physics 201: Lecture 1, Pg 5
Current Loop Physics 201: Lecture 1, Pg 6
Current Loop is a Magnetic Dipole Physics 201: Lecture 1, Pg 7
RHR Physics 201: Lecture 1, Pg 8
Right Hand Rule B-field = magnetic field B-field Right-hand rule Find the B-field for current carrying loop: Fingers in direction of current Thumb gives direction of B-field Physics 201: Lecture 1, Pg 9
Clicker Question 3.5: The diagram below shows a current loop perpendicular to the page; the view is a slice through the loop. The direction of the current in the wire at the top and the bottom is shown. What is the direction of the magnetic field at a point in the center of the loop? A. To the left B. Up C. To the right D. Down Physics 201: Lecture 1, Pg 10
Magnetic Dipole Moment The magnetic dipole moment of a current loop enclosing an area A is defined as: Physics 201: Lecture 1, Pg 11
Clicker Question 2: What is the current direction in the loop? A. Out at the top, in at the bottom. B. In at the top, out at the bottom. C. Either A or B would cause the current loop and the bar magnet to repel each other. Physics 201: Lecture 1, Pg 12
Clicker Question 3: Does the bar magnet attract, repel, or have no effect on the loop? A. Attract B. Repel C. No effect Physics 201: Lecture 1, Pg 13
Clicker Question: The diagram below shows slices through two adjacent current loops. Think about the force exerted on the loop on the right due to the loop on the left. The force on the right loop is directed A. to the left. B. up. C. to the right. D. down. Physics 201: Lecture 1, Pg 14
Line Integrals Figure (a) shows a curved line from i to f. The length l of this line can be found by doing a line integral: Physics 201: Lecture 1, Pg 15
Line Integrals Physics 201: Lecture 1, Pg 16
Line Integrals Physics 201: Lecture 1, Pg 17
What is the line integral of Example: between points i and f, in the figure? Physics 201: Lecture 1, Pg 18
Ampere s Law We know a little bit about finding the B-field if we know what the moving charges are doing Now we will learn a technique to find what the charges are doing based on the B-field This is called Ampere s law Physics 201: Lecture 1, Pg 19
Clicker Question 4: (Ampere s Law) A long, straight wire extends into and out of the screen. The current in the wire is A. Into the screen. B. Out of the screen. C. There is no current in the wire. D. Not enough info to tell the direction. Physics 201: Lecture 1, Pg 20
Ampere s Law Because the B-field is tangent to the circle and of constant magnitude at every point on the circle, we can write: Here B 0 I/2 d, where I is the current through h this loop, hence: Physics 201: Lecture 1, Pg 21
Whenever total current I through passes through h an area bounded by a closed curve, the line integral of the magnetic field around the curve is given by Ampère s law: Ampere s Law Physics 201: Lecture 1, Pg 22
Clicker Question 5: For the path shown, A. 0. B. 0 (I 1 I 2 ). C. 0 (I 1 I 2 ). D. 0 (I 2 I 1 ). Physics 201: Lecture 1, Pg 23
The value of Clicker Question 6: 1.38 10-5 T m around the closed path in the figure. What is I 3. Physics 201: Lecture 1, Pg 24
Ampere s Law Physics 201: Lecture 1, Pg 25
Solenoids Physics 201: Lecture 1, Pg 26
Solenoid Physics 201: Lecture 1, Pg 27
Solenoids: Ampere s Law Physics 201: Lecture 1, Pg 28
Solenoids: Ampere s Law Physics 201: Lecture 1, Pg 29
Solenoids: B Magnitude Magnitude of field inside of solenoid : B= ni n is the number of turns of wire/meter on solenoid. For example, if there are 8 turns and the solenoid is 5 cm long, n 8 turns.05 meter 160 turns / m Physics 201: Lecture 1, Pg 30
Solenoids: B Magnitude Physics 201: Lecture 1, Pg 31
Clicker Question 7: Solenoid 2 has twice the diameter, twice the length, and twice as many turns as solenoid 1. How does the field B 2 at the center of solenoid 2 compare to B 1 at the center of solenoid 1? A. B 2 B 1 /4. B. B 2 B 1 /2. C. B 2 B 1. D. B 2 2B 1. E. B 2 4B 1. Physics 201: Lecture 1, Pg 32
Clicker Question 8: The current in this solenoid A. Enters on the left, leaves on the right. B. Enters on the right, leaves on the left. C. Either A or B would produce this field. Physics 201: Lecture 1, Pg 33
Solenoid A uniform magnetic field can be generated with a solenoid. A solenoid is a helical coil of wire with the same current I passing through each loop in the coil. Solenoids may have hundreds or thousands of coils, often called turns, sometimes wrapped in several layers. The magnetic field is strongest t and most uniform inside the solenoid. Physics 201: Lecture 1, Pg 34
Solenoid The magnetic field outside a solenoid looks like that of a bar magnet. Thus a solenoid is an electromagnet, and you can use the right-hand rule to identify the north-pole end. Physics 201: Lecture 1, Pg 35
MRI This patient is undergoing magnetic resonance imaging (MRI). The large cylinder surrounding the patient contains a solenoid that is wound with superconducting wire to generate a strong uniform magnetic field. Physics 201: Lecture 1, Pg 36
Clicker Question 9: What is the net force between the two solenoids? (a) Attractive (b) Repulsive (c) No force Physics 201: Lecture 1, Pg 37