12.3-Force on a Current Carrying Conductor in a Magnetic Field

12.3-Force on a Current Carrying Conductor in a Magnetic Field Important Formulae

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Grade 10 → Science → Magnetic Effects of Electric Current → 12.3-Force on a Current Carrying Conductor in a Magnetic Field

The interaction between a current-carrying conductor and a magnetic field results in the generation of a force. This principle is the foundation for many electromechanical devices, such as electric motors. Understanding the force experienced by a conductor in a magnetic field is crucial for various applications in technology and physics.

Concept of Force on a Current Carrying Conductor

When an electric current flows through a conductor placed in a magnetic field, a mechanical force acts on the conductor. This phenomenon can be explained by the Lorentz force law, which states that a charged particle moving through a magnetic field experiences a force. The force on the conductor depends on several factors:

  • Magnitude of the Current (I): The force increases with an increase in the current flowing through the conductor.
  • Strength of the Magnetic Field (B): A stronger magnetic field results in a greater force acting on the conductor.
  • Length of the Conductor (L): The longer the conductor within the magnetic field, the greater the force exerted on it.
  • Angle between the Conductor and Magnetic Field: The angle at which the conductor is positioned relative to the magnetic field affects the force experienced by the conductor.
Formula for the Force

The force (\( F \)) on a current-carrying conductor in a magnetic field can be expressed mathematically as:

F = BIL sin(θ)

where:

  • F: Force in newtons (N)
  • B: Magnetic field strength in teslas (T)
  • I: Current in amperes (A)
  • L: Length of the conductor in meters (m)
  • θ: Angle between the direction of the magnetic field and the direction of the current.
Direction of the Force

The direction of the force can be determined using the right-hand rule:

  • Extend your right hand so that your thumb points in the direction of the current (I).
  • Your fingers should point in the direction of the magnetic field (B).
  • Your palm will then face in the direction of the force (F) acting on the conductor.
Applications of Force on Current-Carrying Conductors

The principle of force on current-carrying conductors is widely used in various applications, including:

  • Electric Motors: The force generated by the interaction of magnetic fields and current is harnessed to produce rotational motion.
  • Speakers: The varying current in the coil generates forces that move the diaphragm, producing sound waves.
  • Galvanometers: Instruments that measure electric current by detecting the force on a coil in a magnetic field.
Factors Affecting the Force

The force experienced by a current-carrying conductor can be influenced by several factors:

  • Type of Material: Different materials may have different electrical resistivities, affecting the current flow and thus the force experienced.
  • Temperature: As temperature changes, the resistance of the conductor may change, impacting the current and force.
  • Configuration of the Circuit: The arrangement of the circuit can affect the amount of current flowing through the conductor, thus affecting the force.
Example Calculation

For a conductor of length 0.5 m carrying a current of 3 A placed in a magnetic field of strength 0.2 T at an angle of 90° to the field:

  • Using the formula: F = BIL sin(θ)
  • F = 0.2 T × 3 A × 0.5 m × sin(90°)
  • F = 0.2 × 3 × 0.5 × 1 = 0.3 N
  • The force acting on the conductor is 0.3 N.


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12.3-विद्युत धारा वाले चालक पर चुम्बकीय क्षेत्र में बल

चुम्बकीय क्षेत्र में विद्युत धारा चलाने पर उस पर एक बल कार्य करता है। यह बल चुम्बकीय क्षेत्र और विद्युत धारा के संयोजन से उत्पन्न होता है। इसे "चुम्बकीय बल" कहते हैं।

चुम्बकीय बल का सूत्र

चुम्बकीय क्षेत्र में विद्युत धारा वाले चालक पर जो बल कार्य करता है, उसे निम्नलिखित सूत्र से व्यक्त किया जा सकता है:

F = B I l sinθ

  • F: बल (Newton)
  • B: चुम्बकीय क्षेत्र की तीव्रता (Tesla)
  • I: विद्युत धारा (Ampere)
  • l: चालक का लंबाई (Meter)
  • θ: चुम्बकीय क्षेत्र रेखाओं और चालक के बीच का कोण

यह सूत्र बताता है कि विद्युत धारा वाले चालक पर बल की दिशा और उसकी तीव्रता चुम्बकीय क्षेत्र की दिशा, विद्युत धारा की दिशा, और चालक की लंबाई पर निर्भर करती है।

बल की दिशा

चुम्बकीय बल की दिशा का निर्धारण फлемिंग के बाएं हाथ के नियम द्वारा किया जा सकता है। इस नियम के अनुसार:

  • अपने बाएं हाथ की तीनों अंगुलियों को इस प्रकार रखें कि:
  • पहली अंगुली चुम्बकीय क्षेत्र (B) की दिशा को दिखाए,
  • दूसरी अंगुली विद्युत धारा (I) की दिशा को दिखाए,
  • तब मध्यमा अंगुली उस बल की दिशा को दिखाएगी, जो चालक पर कार्य करता है।
चुम्बकीय क्षेत्र में बल की उत्पत्ति

चुम्बकीय क्षेत्र में चालक पर बल उत्पन्न होता है क्योंकि जब विद्युत धारा किसी चुम्बकीय क्षेत्र से गुजरती है, तो चुम्बकीय क्षेत्र उसके चारों ओर बल पैदा करता है। यह बल चालक पर एक यांत्रिक प्रभाव डालता है।

चुम्बकीय बल का प्रभाव

जब चालक चुम्बकीय क्षेत्र में रखा जाता है और उसमें विद्युत धारा बहती है, तो उस पर बल कार्य करता है। यह बल चालक को चुम्बकीय क्षेत्र के अनुरूप एक दिशा में धकेलता है। बल का आकार और दिशा विद्युत धारा और चुम्बकीय क्षेत्र की तीव्रता पर निर्भर करता है।

महत्वपूर्ण बिंदु
  • चुम्बकीय क्षेत्र और विद्युत धारा के बीच का कोण (θ) महत्वपूर्ण होता है। यदि θ = 90° है, तो sinθ = 1, और बल अधिकतम होता है।
  • यदि θ = 0° है, तो sinθ = 0, और बल शून्य होता है।
  • यदि चालक की लंबाई और चुम्बकीय क्षेत्र की तीव्रता अधिक होती है, तो बल भी अधिक होगा।

A positively-charged particle (alpha-particle) projected towards west is deflected towards north by a magnetic field. The direction of magnetic field is

Solution:

Direction of Magnetic Field for Deflection of Alpha Particle

When a positively-charged particle, such as an alpha particle, is projected towards the west and is deflected towards the north by a magnetic field, we can determine the direction of the magnetic field using the right-hand rule. According to this rule, if you point your thumb in the direction of the velocity of the charged particle (west) and your fingers in the direction of the force acting on the particle (north), then your palm will face in the direction of the magnetic field. Thus, the magnetic field is directed downwards, towards the Earth's surface.

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Which of the following property of a proton can change while it moves freely in a magnetic field? (There may be more than one correct answer.)
(a) mass
(b) speed

(c) velocity
(d) momentum

Solution:

Properties of a Proton in a Magnetic Field

When a proton moves freely in a magnetic field, certain properties can change due to the influence of the magnetic force. The speed (b) of the proton can change as it experiences acceleration perpendicular to its motion. Consequently, the velocity (c) will also change, as velocity is a vector quantity that depends on both speed and direction. Furthermore, momentum (d), which is the product of mass and velocity, can also change due to changes in speed and direction. However, the mass (a) of the proton remains constant during this motion.

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In Activity 12.7, how do we think the displacement of rod AB will be affected if (i) current in rod AB is increased; (ii) a stronger horse-shoe magnet is used; and (iii) length of the rod AB is increased?

Solution:

Effect on Displacement of Rod AB in Activity 12.7

(i) If the current in rod AB is increased, the displacement will also increase because a higher current generates a stronger magnetic force on the rod. (ii) Using a stronger horse-shoe magnet will enhance the magnetic field strength, leading to greater displacement of the rod AB as the interaction between the magnetic field and the current increases. (iii) Increasing the length of rod AB will result in greater displacement, as a longer rod experiences a larger area affected by the magnetic field, thus increasing the overall force acting on it.

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