Force on a Current Carrying Conductor in a Magnetic Field | Jamb(UTME)

Jamb(utme) key points on quantitative treatment of force between two parallel current-carrying conductors; force on a charge moving in a magnetic field; the d. c. motor

Quantitative Treatment of Force Between Two Parallel Current-Carrying Conductors

1. Parallel current-carrying conductors exert a force on each other due to their magnetic fields.
2. If the currents flow in the same direction, the conductors attract each other.
3. If the currents flow in opposite directions, the conductors repel each other.
4. The force per unit length $F/L$ between two conductors is proportional to the product of their currents.
5. The formula for the force per unit length is:
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   $\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2 \pi d}$
   where:
   • $\mu_0$: Permeability of free space #$(4 \pi \times 10^{-7}T·m/A)$,
   • $I_1, I_2$: Currents in the two conductors,
   • $d$: Distance between the conductors.
6. The force is inversely proportional to the distance $d$ between the wires.
7. The SI unit of the force is Newton (N).
8. The direction of the force is determined by the right-hand rule for magnetic fields.
9. The force increases if the currents are increased.
10. If one of the conductors carries no current, there is no magnetic force.
11. This phenomenon is the basis for defining the ampere, the SI unit of current.
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Force on a Charge Moving in a Magnetic Field

12. A moving charge in a magnetic field experiences a force known as the Lorentz force.
13. The magnitude of the force is given by:
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    $F = qvB \sin \theta$ where:
    • $F$: Magnetic force,
    • $q$: Charge of the particle,
    • $v$: Velocity of the particle,
    • $B$: Magnetic field strength,
    • $\theta$: Angle between the velocity vector and magnetic field.
14. If $\theta = 0^\circ$ or $180^\circ$, the force is zero because the charge moves parallel to the field.
15. If $\theta = 90^\circ$, the force is maximum.
16. The direction of the force is perpendicular to both the velocity of the charge and the magnetic field.
17. The force's direction is determined using the right-hand rule: point your fingers in the direction of velocity, curl them towards the magnetic field, and your thumb points to the force.
18. Positive charges follow the direction of the force; negative charges move in the opposite direction.
19. This force causes charged particles to move in circular or helical paths in a magnetic field.
20. The radius of the circular path is:
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    $r = \frac{mv}{qB}$ where $m$ is the mass of the charged particle.
21. The force is responsible for the motion of particles in devices like cyclotrons.
22. Magnetic force does no work on the charge because it acts perpendicular to the velocity.
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The D.C. Motor

23. A D.C. motor converts direct current electrical energy into mechanical energy.
24. The principle behind a D.C. motor is the force exerted on a current-carrying conductor in a magnetic field.
25. The main components are:
    • Armature (a coil of wire),
    • Magnetic field (produced by permanent magnets or electromagnets),
    • Commutator,
    • Brushes.
26. The armature is placed between the poles of the magnetic field.
27. When current flows through the armature, it experiences a force due to the magnetic field.
28. The direction of the force is determined by Fleming's left-hand rule.
29. According to the rule, point your first finger in the direction of the magnetic field, your second finger in the direction of current, and your thumb will point in the direction of motion (force).
30. The force on the armature causes it to rotate.
31. The rotation continues due to the commutator, which reverses the current's direction in the armature after each half-turn.
32. This reversal ensures that the torque (rotational force) always acts in the same direction.
33. The speed of the motor depends on the supply voltage and the strength of the magnetic field.
34. Increasing the number of turns in the coil increases the motor's efficiency.
35. The torque $\tau$ produced by the motor is proportional to the current:
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    $\tau = BINA$ where:
    • $B$: Magnetic field strength,
    • $I$: Current,
    • $N$: Number of turns in the coil,
    • $A$: Area of the coil.
36. D.C. motors are classified as series motors or shunt motors, depending on the winding configuration.
37. Series motors provide high torque at low speeds, making them suitable for heavy loads.
38. Shunt motors have nearly constant speed and are used in applications like fans.
39. The efficiency of a D.C. motor can be improved by using strong magnets and reducing friction.
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Applications of D.C. Motors

40. Used in household appliances like fans, blenders, and vacuum cleaners.
41. Essential in industrial machines requiring precise torque control.
42. Used in electric vehicles for efficient power conversion.
43. Integral to robotics and automated systems.
44. Found in toys like remote-controlled cars.
45. Employed in elevators and escalators for smooth operation.
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Real-World Applications of Magnetic Forces

46. Magnetic forces are used in particle accelerators to study subatomic particles.
47. They play a crucial role in designing cyclotrons and synchrotrons.
48. Electric generators use principles similar to D.C. motors but operate in reverse to produce electricity.
49. Electromagnetic railguns use magnetic forces to launch projectiles at high speeds.
50. Magnetic levitation (maglev) trains rely on magnetic forces to achieve frictionless motion.
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Jamb(utme) key points on magnetic field of electromagnets; carbon microphone;moving coil and moving iron instruments

Magnetic Field of Electromagnets

1. Electromagnets are created by passing electric current through a coil of wire.
2. The magnetic field is strongest inside the coil and weaker outside.
3. The magnetic field strength increases with the number of turns in the coil.
4. Increasing the current in the coil also strengthens the magnetic field.
5. A soft iron core inside the coil enhances the magnetic field.
6. The field produced by an electromagnet is temporary and exists only while current flows.
7. Electromagnets can be switched on and off by controlling the current.
8. The direction of the magnetic field is determined by the right-hand rule.
9. The poles of the electromagnet depend on the direction of current in the coil.
10. Electromagnets are widely used in devices like motors, relays, and cranes.
11. Electromagnets in electric bells attract an armature to ring the bell.
12. Electromagnets in maglev trains allow frictionless and high-speed travel.
13. The strength of an electromagnet is adjustable, making it versatile.
14. Electromagnets are safer than permanent magnets in high-power applications.
15. They are used in MRI machines to create strong magnetic fields for medical imaging.
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Carbon Microphone

16. A carbon microphone converts sound waves into electrical signals.
17. It uses a diaphragm connected to a container filled with carbon granules.
18. Sound waves strike the diaphragm, causing it to vibrate.
19. The vibrations compress and decompress the carbon granules.
20. The resistance of the carbon granules changes with compression.
21. A battery provides a steady current through the carbon granules.
22. Changes in resistance cause variations in the current, creating an electrical signal.
23. The signal corresponds to the sound wave's frequency and amplitude.
24. Carbon microphones are sensitive and pick up low sound levels well.
25. They were widely used in early telephones for voice transmission.
26. Carbon microphones are simple and inexpensive to manufacture.
27. Their design makes them durable and resistant to damage.
28. They have been replaced in many applications by modern microphones but are still used in certain industries.
29. Carbon microphones are effective for low-frequency sound applications.
30. Their output is amplified for use in audio and communication systems.
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Moving Coil Instruments

31. Moving coil instruments measure current or voltage using a coil in a magnetic field.
32. The coil is mounted on a pivot and can rotate freely.
33. When current flows through the coil, it generates a magnetic field.
34. This field interacts with a permanent magnet’s field, causing the coil to rotate.
35. The rotation is proportional to the current passing through the coil.
36. A pointer attached to the coil moves over a calibrated scale to display readings.
37. Moving coil instruments are very sensitive and accurate.
38. They work only with direct current (DC) because alternating current (AC) causes the pointer to fluctuate.
39. The coil is wound on a lightweight aluminum frame to minimize inertia.
40. A hair spring provides a restoring force and controls the pointer's movement.
41. Moving coil instruments are used in voltmeters and ammeters.
42. They are best suited for low-current and low-voltage measurements.
43. Damping mechanisms prevent the pointer from oscillating excessively.
44. Moving coil instruments provide precise and steady readings.
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Moving Iron Instruments

45. Moving iron instruments measure current or voltage by the movement of a piece of iron.
46. They are based on the principle of magnetic attraction or repulsion of the iron piece.
47. A coil carries the current to be measured and produces a magnetic field.
48. The field attracts or repels a soft iron piece, moving it.
49. The movement of the iron piece is transferred to a pointer that moves over a scale.
50. Moving iron instruments can work with both AC and DC.
51. They are less sensitive than moving coil instruments but more versatile.
52. These instruments are robust and durable, suitable for industrial applications.
53. The readings are slightly nonlinear due to the magnetic properties of the iron.
54. Moving iron instruments are commonly used in ammeters and voltmeters.
55. They can handle higher currents and voltages than moving coil instruments.
56. Damping mechanisms prevent pointer oscillations, ensuring steady readings.
57. The construction is simpler, making them cost-effective.
58. They are widely used in power stations and electrical distribution systems.
59. Moving iron instruments are less precise than moving coil instruments but sufficient for general purposes.
60. They are reliable and can withstand harsh environmental conditions.
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Jamb(utme) key points on conversion of galvanometers to ammeters and voltmeter using shunts and multipliers; sensitivity of a galvanometer

Conversion of Galvanometers to Ammeters and Voltmeters

Converting a Galvanometer to an Ammeter

1. A galvanometer measures small currents, but it cannot measure large currents directly.
2. To convert a galvanometer into an ammeter, a shunt resistor is connected in parallel with the galvanometer.
3. A shunt is a low-resistance device that allows most of the current to bypass the galvanometer.
4. The value of the shunt resistance is chosen to protect the galvanometer from excessive current.
5. The total current divides between the galvanometer and the shunt according to their resistances.
6. The formula for the shunt resistance is:
   
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   $R_s = \frac{I_g \cdot R_g}{I - I_g}$ where:
   • $R_s$: Shunt resistance,
   • $I_g$: Full-scale deflection current of the galvanometer,
   • $R_g$: Resistance of the galvanometer,
   • $I$: Total current to be measured.
7. A properly designed shunt allows the galvanometer to handle currents much larger than its normal capacity.
8. The ammeter's range depends on the value of the shunt.
9. Ammeters are always connected in series with the circuit to measure current.
10. The galvanometer's needle deflection indicates the proportional current through the entire circuit.
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Converting a Galvanometer to a Voltmeter

11. A galvanometer can be converted to a voltmeter by connecting a multiplier resistor in series with it.
12. The multiplier increases the galvanometer's effective resistance, limiting the current through it.
13. The total resistance of the voltmeter is the sum of the galvanometer resistance and the multiplier resistance.
14. The formula for the multiplier resistance is:
    
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    $R_m = \frac{V}{I_g} - R_g$ where:

• $R_m$: Multiplier resistance,
• $V$: Voltage to be measured,
• $I_g$: Full-scale deflection current of the galvanometer,
• $R_g$: Resistance of the galvanometer.

15. The voltmeter's range depends on the value of the multiplier.
16. Voltmeters are connected in parallel with the component to measure the voltage drop across it.
17. The galvanometer's deflection corresponds to the voltage across the multiplier.
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Key Points About Conversions

18. A galvanometer has a low resistance, making it unsuitable for direct voltage or high current measurements.
19. Adding shunts and multipliers makes the galvanometer versatile for different measurements.
20. Shunts and multipliers are carefully calibrated to ensure accurate readings.
21. Proper conversion ensures the galvanometer does not get damaged by excessive current or voltage.
22. The accuracy of the converted instrument depends on the precision of the shunt and multiplier resistances.
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Sensitivity of a Galvanometer

23. Sensitivity refers to the galvanometer's ability to detect small currents or voltages.
24. The sensitivity is measured in terms of the current or voltage required for full-scale deflection.
25. Current sensitivity $(S_I)$ is defined as the deflection per unit current:
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    $S_I = \frac{\theta}{I}$ where:

• $\theta$: Deflection angle,
• $I$: Current.

26. A galvanometer with high current sensitivity requires a smaller current for a given deflection.
27. Voltage sensitivity $(S_V)$ is defined as the deflection per unit voltage:
    
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    $S_V = \frac{\theta}{V}$
28. Voltage sensitivity depends on both the current sensitivity and the resistance of the galvanometer:
    
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    $S_V = \frac{S_I}{R_g}$
29. High resistance reduces voltage sensitivity but increases the galvanometer's voltage range.
30. Sensitivity can be improved by using stronger magnets for the galvanometer’s magnetic field.
31. Increasing the number of turns in the galvanometer coil enhances sensitivity.
32. A lightweight coil reduces inertia, improving sensitivity.
33. The torsional constant of the suspension wire affects the sensitivity; softer wires improve it.
34. Damping mechanisms prevent oscillations, ensuring stable readings without sacrificing sensitivity.
35. A more sensitive galvanometer is better for detecting small changes in current or voltage.
36. High sensitivity is essential for applications like bridge circuits and weak signal detection.
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Practical Considerations for Sensitivity

37. Excessive sensitivity can make the instrument unstable or prone to external interference.
38. In practical applications, sensitivity is balanced with the instrument's range and stability.
39. A sensitive galvanometer may require shielding to protect against stray magnetic fields.
40. Sensitivity is reduced when converting a galvanometer to an ammeter because of the shunt's low resistance.
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Advantages and Limitations

41. Converted galvanometers are cost-effective for specific measurement purposes.
42. They are less accurate than dedicated ammeters or voltmeters but serve well in general applications.
43. High sensitivity galvanometers are fragile and require careful handling.
44. Inaccuracy can arise from temperature variations affecting the resistance of shunts and multipliers.
45. Proper calibration is essential to maintain accuracy after conversion.
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Applications of Sensitive Galvanometers

46. Sensitive galvanometers are used in bridge circuits to detect null points.
47. They are vital in laboratories for precise current and voltage measurements.
48. In physics experiments, galvanometers help study weak electrical signals.
49. They are used in electrometers to measure very low currents and voltages.
50. Sensitive galvanometers are also part of magnetic and electrochemical research.
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