6.3 Magnetic Force and Field (4 hr)

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1 6.3 Magnetic Force and Field (4 hr) Name Activity 631 Investigating Magnetic Field around a magnet Activity 632 Investigating Electric Field in a slinky. Activity 633 Build your own Electric Motor. Read Tsokos pp Read Cutnell pp Assignment A631 (1) Tsokos pp #1 to 17, 26, 30, 31, 32 (2) Cutnell pp pp 674, 675 # 14, 15, 23 (3) Ranking pp

2 Magnet and Magnetic Field A. Magnet There are always two poles on a magnet Poles of magnets (1) (2) Only the following materials have magnetic properties Soft magnetic materials: iron Hard magnetic material: cobalt and nickel B. Magnetic Field Magnetic field has direction and magnitude; it is a vector. The direction of magnetic field is determined by the effect it has on a compass needle (i.e. a small bar magnet), <Sample question> A magnetic needle aligns itself in the direction of the magnetic vector. Identify the direction of the magnetic field when the following compasses placed in different magnetic fields: 2

3 C. Magnetic Field Lines Magnetic field is invisible and can work at a distance. Magnetic field lines are created to help us visualize the magnetic field. Rules for magnetic field lines (1) Magnetic field lines are tangent to the magnetic field at every point; (2) Outside of a magnet: Magnetic field lines point away from the north pole of a magnet and toward its south pole; (3) Inside of a magnet: Magnetic field lines point toward the north pole of a magnet and away from its south pole; (4) The number of magnetic field lines is proportional to the magnitude of the field; (5) Magnetic field lines always form closed loops. The Pattern of magnetic field (lines) can be displayed by fine iron filings or compasses D. Earth s Magnetic Earth is a giant magnet 3

4 Examples of magnetic field lines (1) Single magnet (2) Unlike poles facing each other (3) Like poles facing each other 4

5 Moving Charge and Magnetic Field The moving charges give rise to magnetic field. A static electric field creates an electric field, and A moving charge creates an electric field and a magnetic field. The field from a point charge whose velocity is small compared to the speed of light is expressed as We are focused on finding the strength and direction of the instantaneous magnetic field that is on the plane around the charge. The magnitude of magnetic field induced by a moving charge is directly proportional to the q and v, and inversely proportional to r 2 Direction: apply Right Hand Rule Bird s view Summary 5

Magnetic Field Patterns due to Current (Ampere s Law) The induced magnetic field due to a current-carrying wire A current in a straight line produces a magnetic field around it.

Ørsted discovered that: The magnitude of the field B created by the current in a wire varies linearly with the current in the wire and inversely with the perpendicular distance from the wire.

6 Magnetic Field Patterns due to Current (Ampere s Law) The induced magnetic field due to a current-carrying wire A current in a straight line produces a magnetic field around it. The Danish scientist H. C. Ørsted discovered that: The magnitude of the field B created by the current in a wire varies linearly with the current in the wire and inversely with the perpendicular distance from the wire. The magnitude is stated by Ampere s Law: B dl I l o closed For a long, straight wire, the magnetic field, B is: B = o I / 2 r where, o = 4 x 10-7 T m / A and is called the permeability of free space, r is the radial distance from the wire in meters, and I is the current in amperes. SI unit: Tesla, T The direction: RHR Using your right-hand: Curl your fingers into a half-circle around the wire, they point in the direction of the magnetic field, B. Point your thumb in the direction of the conventional current. Summary 6

7 (a) Magnetic Field Lines around a long current-carrying wire The density of magnetic field lines depends on the magnitude of the magnetic field. Video for calculating magnetic field around a current-carry wire: The unit Tesla is a big unit; The magnetic field of the earth is about 10 4 T on the earth s surface. A wire carrying a current of 2000 A produces a magnetic field of 8x10 5 T at a distance of 5 m from the wire. When the current is perpendicular to the plane as shown, x sign represent current going into paper, the sign coming out Summary 7

8 <Sample Questions> 1. Determine the direction and the magnitude of the magnetic field at position p, and the magnetic field lines created by a current-carrying wire. µ 0 = 4π 10 7 V s/(a m) (a) (b) (c) I = 3.2 A (d) I= 5.0 A 2. Find the current in a long straight wire that would produce a magnetic field twice the strength of the Earth s at a distance of 5.0 cm from the wire. (The Earth s field is about T) 8

9 (b) The magnetic field induced by a flat circular coil The magnetic field accumulated from segments of a flat coil at the center of the circle is expressed as or if there are n loops <Sample Question> 3. A flat circular coil with 10 turns, a radius of 2.24 x10-2 m, and a current of 1.5A in the circular wire. Find the magnetic field at the center of the flat loop. 4. Find the direction of magnetic field in the following circular current-carrying wires. Summary 9

(c) The magnetic field induced by a solenoid A long straight coil of wire can be used to generate a nearly uniform magnetic field similar to that of a bar magnet.

Direction of B: RHR2 Magnitude of the B field in the center of the solenoid: B = μ 0 n I Where o = 4 x 10-7 T m / A, I is the current, and L>>2r n is the number of loops per unit length; n = number

10 (c) The magnetic field induced by a solenoid A long straight coil of wire can be used to generate a nearly uniform magnetic field similar to that of a bar magnet. Such coils, called solenoids, have an enormous number of practical applications. The field can be greatly strengthened by the addition of an iron core. Such cores are typical in electromagnets. Direction of B: RHR2 Magnitude of the B field in the center of the solenoid: B = μ 0 n I Where o = 4 x 10-7 T m / A, I is the current, and L>>2r n is the number of loops per unit length; n = number of loops/length of the solenoid In the above expression for the magnetic field B, n is the number of turns per unit length, sometimes called the "turns density". The expression is an idealization to an infinite length solenoid, but provides a good approximation to the field of a long solenoid. <Sample Question> 5. For a 20 cm long Solenoid with 100 turns, if the current in it is 4.0A, what is the strength and direction of magnetic field in the center of the solenoid? 10

6. Determine the strength and direction of magnetic field in the center of the solenoid, and the

strength of the magnetic field at V = 9V, R wire = 1.

0A; n= field in the center of the nail and the direction of 20 turns/m. the compasses.

11 6. Determine the strength and direction of magnetic field in the center of the solenoid, and the direction of North Pole of the compass (a) Label the N and S poles of the electromagnet (b) Find the strength of the magnetic field at V = 9V, R wire = 1.2 ohms, find the magnetic the center of the solenoid. I = 3.0A; n= field in the center of the nail and the direction of 20 turns/m. the compasses. (c) Find the magnetic field at the center of the solenoid and the direction of the current. (d) Determine the direction of the current in the wire and the magnitude of the magnetic field at the center of the solenoid. (I= 2.2A) 11

12 7. Find the magnetic field at point P that is 10 cm below the wire with 1.5 A in the following diagram. Application of Electromagnet Strong junk yard electromagnet Summary 12

Magnetic Force on a Current-Carrying Conductor in a Magnetic Field If a current-carrying wire is placed in a region of magnetic field, it will experience a magnetic force.

to find direction of the magnetic force acting on the current-carrying wire or moving charges.

13 Magnetic Force on a Current-Carrying Conductor in a Magnetic Field If a current-carrying wire is placed in a region of magnetic field, it will experience a magnetic force. Magnetic Force on a Current-Carrying Wire is expressed as Where is the angle between I and B Magnitude of the Magnetic Force, F B : Right Hand Rule 1 The right-hand-rule #1 is applied to find direction of the magnetic force acting on the current-carrying wire or moving charges. This RHR 1 shows that the magnetic force is always perpendicular to the plane that the directions of both B and I are on. The acronym FBI is easy to remember, but this way may only used for cases in which the current-carrying wire and the magnetic field are normal to each other: 13

directed into paper, F B is to the left. 2.

Depending on the direction of the current,

14 <Examples> 1. A wire with current I is placed in a B directed into paper, F B is to the left. 2. A wire with current I is placed in a B directed to the right, F B is going up. 3. The bar is placed on bare wires and may slide freely on the wires. 4. Depending on the direction of the current, the wire is stretched to different directions. 14

15 8. In the following questions, B = 2.5x10 5 T, I = 1.6A. Find the magnetic force acting on per unit length of the wire. (find the B-force per meter) 15

Direction of Magnetic Force on a charge moving in a Magnetic Field Conventional Current is a stream of positive charges, similar to the effect from a magnetic field

Magnitude of Magnetic Force on a moving charge Where is the angle between v and B The RHR1 is for the positive moving charge.

16 Direction of Magnetic Force on a charge moving in a Magnetic Field Conventional Current is a stream of positive charges, similar to the effect from a magnetic field on current, a moving charge in a magnetic field experiences magnetic force acting on it. Magnitude of Magnetic Force on a moving charge Where is the angle between v and B The RHR1 is for the positive moving charge. For the negative moving charge, use left hand or reverse the moving direction first before apply RHR1. The FBI hand rule is for the positive moving charge. For the negative moving charge, use left hand or reverse the moving direction first before apply FBI hand rule. Summary 16

<Examples> The positive charge moving to the right in a magnetic field B that is into the

F B = qvb The path of the positive charge would be curved due to the magnetic force.

charges are deflected when moving in a magnetic field.

17 <Examples> The positive charge moving to the right in a magnetic field B that is into the paper experiences a magnetic force pulling it upwards. F B = qvb The path of the positive charge would be curved due to the magnetic force. The Magnetic Force = Centripetal Force qvb = mv 2 /r The paths of the positive and negative charges are deflected when moving in a magnetic field. The path of a moving neutral particle is not affected. When a charge enters a magnetic field at an angle (the angle between v and B is not 90 o ), the charge moves along a helical path. 17

magnetic field at a speed of 200 m s 1 as shown. 10.

18 Application: motor <Sample Questions> 9. Find the magnetic force acting on the electron moving in a 50 T magnetic field at a speed of 200 m s 1 as shown. 10. A 5 nc charge moving with 300 m s 1 in a 120T magnetic field. Find the magnetic force acting on it. 18

19 11. A 20 μc charge moving at 250 m s 1 heading north enters a magnetic field of 120T that goes into the plane as shown. (a) Is the charge positive or negative? (b) Find the radius of the circular path. (The mass of the particle is 50 nanograms) 12. A 16 μc charge moving at 200 m s 1 enters a region that contains a uniform electric field E of 500 N C 1 and a magnetic field B. The path of the charge is not deflected. The charge goes through the region along a straight line. Determine the magnitude of the magnetic field. Summary 19

= I 2 B 1 =. (a) Is the magnetic force repulsive or attracted?

20 13. Two parallel current-carrying conductors would either repel or attract each other. I 2 lies in the magnetic field created by I 1 that is into the paper, force on I 2, F B2/l = I 2 B 1 =. (a) Is the magnetic force repulsive or attracted? (b) What o=is the magnitude of the magnetic force per meter?, so the magnetic 14. State the definition of magnetic field. 20

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22 The definition of magnetic Field: 22

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Chapter 27, 28 & 29: Magnetism & Electromagnetic Induction

Chapter 27, 28 & 29: Magnetism & Electromagnetic Induction The Magnetic Field The Magnetic Force on Moving Charges The Motion of Charged Particles in a Magnetic Field The Magnetic Force Exerted on a Current-Carrying