2. 1© Manhattan Press (H.K.) Ltd. 16.6 magnetic fields due to currents Long straight wire Circular coil Long solenoid

3. 2 © Manhattan Press (H.K.) Ltd. 16.6 Magnetic fields due to current (SB p. 219) Long straight wire 1. By right-hand grip rule If the wire is grasped in the right hand with the thumb in the direction of the current, then the fingers curl pointing in the direction of the magnetic field.

4. 3 © Manhattan Press (H.K.) Ltd. 16.6 Magnetic fields due to current (SB p. 220) Long straight wire 2. Magnetic flux density (B)  0 = permeability of free space = 4  x 10 -7 T m A -1

5. 4 © Manhattan Press (H.K.) Ltd. 16.6 Magnetic fields due to current (SB p. 220) Long straight wire 3. Experimental set-up - B  I - B  1/r Notes: 1. The wire should be long. 2. The distance (r) is small compared with the length of the wire. 3. The wire should be placed along the direction of the Earth’s magnetic field (north- south direction) to reduce the effect due to the Earth’s magnetic field. Go to Example 6 Example 6

6. 5 © Manhattan Press (H.K.) Ltd. 16.6 Magnetic fields due to current (SB p. 222) Circular coil

7. 6 © Manhattan Press (H.K.) Ltd. 16.6 Magnetic fields due to current (SB p. 222) Circular coil 1. Right-hand grip rule Curl the fingers of the right hand in the direction of the current, and the thumb will point in the direction of the magnetic field inside the coil.

8. 7 © Manhattan Press (H.K.) Ltd. 16.6 Magnetic fields due to current (SB p. 223) Circular coil 2. Magnetic flux density (B) - magnetic flux density at centre of coil 3. Experimental set-up (a) B  I and N (b) B  1/r Note: The magnetic field is the maximum at the centre of the circular coil. Go to Example 7 Example 7

9. 8 © Manhattan Press (H.K.) Ltd. 16.6 Magnetic fields due to current (SB p. 224) Long solenoid 1. Magnetic field produced by a long solenoid

10. 9 © Manhattan Press (H.K.) Ltd. 16.6 Magnetic fields due to current (SB p. 225) Long solenoid 2. Right-hand grip rule Curl the fingers of the right hand in the direction of the current, and the thumb will point in the direction of the magnetic field inside the solenoid. Go to More to Know 8 More to Know 8

11. 10 © Manhattan Press (H.K.) Ltd. 16.6 Magnetic fields due to current (SB p. 225) Long solenoid 3. Experimental set-up (a) B  I and N (b) B  1/ Notes: 1. The magnetic field within a solenoid is quite uniform along its axis except near its two ends. 2. The magnetic field within a solenoid is independent of the shape and the cross section area of the solenoid.

12. 11 © Manhattan Press (H.K.) Ltd. 16.6 Magnetic fields due to current (SB p. 226) Long solenoid 4. At the ends of solenoid Note: The magnetic field drops to zero along the axis outside the solenoid.

13. 12 © Manhattan Press (H.K.) Ltd. 16.6 Magnetic fields due to current (SB p. 226) Long solenoid Current- carrying conductor Position of magnetic field Magnetic flux density (B) Symbol 1. Long straight wire Around the wire r = perpendicular distance from wire 2. Circular coil At the centre N = no. of turns r = radius of coil 3. SolenoidInside At the ends N = no. of turns = length of solenoid n = N /

14. 13 © Manhattan Press (H.K.) Ltd. End

15. 14 © Manhattan Press (H.K.) Ltd. Q: Q: Two long rigid wires X and Y each carries a current of 20 A in the directions as shown in the figure. If the distance between the wires is 10 mm, find the magnitude and direction of the magnetic flux density at the points (a) P and (b) Q. 16.6 Magnetic fields due to current (SB p. 221) Solution

16. 15 © Manhattan Press (H.K.) Ltd. Solution: (a) The figure shows the top view of the directions of the magnetic flux density B X and B Y due to the currents in wires X and Y respectively, at the point P. 16.6 Magnetic fields due to current (SB p. 221)

17. 16 © Manhattan Press (H.K.) Ltd. Solution (cont’d): (b) At the point Q, the magnetic flux density due to the currents in X and Y, B X and B Y respectively, are in the same direction and having the magnitudes: Return to Text 16.6 Magnetic fields due to current (SB p. 221)

18. 17 © Manhattan Press (H.K.) Ltd. Q: Q: Two circular coils P and Q lie in the same plane and are concentric. Coil P has 10 turns of radius 5.0 cm and carries a current of 1.0 A. Coil Q has 20 turns of radius 8.0 cm and the current in it is adjusted in magnitude and direction so that the resultant field at the common centre is zero. Draw a diagram to show the relative directions of the currents in the two coils and find the magnitude of the current in coil Q. 16.6 Magnetic fields due to current (SB p. 223) Solution

19. 18 © Manhattan Press (H.K.) Ltd. Solution: The currents in the two coils are in opposite directions. The magnetic flux density at the common centre of the coils due to the currents I 1 and I 2 in the coils P and Q, respectively, are Return to Text 16.6 Magnetic fields due to current (SB p. 224)

20. 19 © Manhattan Press (H.K.) Ltd. Soft-iron piece If a soft-iron piece is inserted into the solenoid, the flux density within the solenoid is: B = μ r μ 0 nI where μ r is a constant known as the relative permeability of soft-iron. Return to Text 16.6 Magnetic fields due to current (SB p. 225)