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Force on a Current Carrying Conductor Placed in a Magnetic Field
A conductor that carries current generates a magnetic field around itself. When this conductor is placed within an external magnetic field, the two magnetic fields interact, resulting in a net force acting on the conductor.
If a conductor of length l, carrying current I, is positioned in a magnetic field with intensity B and forms an angle θ with it, the force on the conductor can be calculated using:
F = IlB sin Θ
If the conductor is lying perpendicular to the magnetic field, then
θ = 90° [sin θ = 1] and the force becomes F = IlB.
This force acts in a direction that is perpendicular to the plane formed by the conductor and the magnetic field, reaching its maximum value. The displacement of the rod is greatest when the current flows at right angles to the magnetic field direction.
If the conductor runs parallel to the magnetic field, then θ = 0° (where sin θ = 0), making the force zero, which is its minimum.
Fleming's Left Hand Rule
The direction of the force on a current-carrying conductor in a magnetic field is described by Fleming's Left Hand Rule. This rule states that:
If you stretch your left hand so that your forefinger, second finger, and thumb are at right angles to each other, with the forefinger pointing in the direction of the magnetic field and the second finger pointing in the direction of the current, the thumb shows the direction of the force. Remember, if the direction of the current changes, the direction of the force will also change.
Factors on which the force acting on the current carrying conductor depends
The force acting on a current carrying conductor is placed in the magnetic field depends upon :
(i) The strength of the magnetic field : If the conductor is placed in a strong magnetic field, it experiences a large force. That is, F∝ B (strength of magnetic field)
(ii) The strength of the electric curent : If large current flows through the conductor placed in the magnetic field, it experiences a large force. That is F ∝ I.
(iii) The length of the conductor : A long conductor experiences a greater force than the short conductor, when placed in the magnetic field. That is, F ∝ ℓ.
That is F∝ BIℓ
or F = kBIl
If k = 1, F = BIℓ
then B = 
If I = 1amp. and l = 1m then B = F
Thus, magnetic field strength (B) is defined as the force acting per unit current per unit length of a conductor placed perpendicular to the direction of the magnetic field.
SI unit of magnetic field strength is Tesla.
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FAQs on Force on a Current Carrying Conductor & Fleming's Left & Right Hand Rule - Science Class 10
| 1. What is Fleming's Left Hand Rule and how is it applied to find the direction of force on a current-carrying conductor in a magnetic field? |  |
Ans. Fleming's Left Hand Rule is a mnemonic device used to determine the direction of the force experienced by a current-carrying conductor in a magnetic field. According to this rule, if you align your thumb, index finger, and middle finger of your left hand perpendicular to each other, with the index finger pointing in the direction of the magnetic field (from North to South), and the middle finger pointing in the direction of the current (from positive to negative), then your thumb will point in the direction of the force (motion) experienced by the conductor.
| 2. What factors affect the magnitude of the force on a current-carrying conductor placed in a magnetic field? | |
Ans. The magnitude of the force on a current-carrying conductor in a magnetic field is influenced by several factors:
1. The strength of the magnetic field (B): A stronger magnetic field results in a greater force.
2. The amount of current flowing through the conductor (I): More current increases the force experienced.
3. The length of the conductor within the magnetic field (L): A longer conductor segment in the field results in a larger force.
4. The angle between the conductor and the magnetic field: The force is maximized when the conductor is perpendicular to the magnetic field and is given by the formula F = BIL sin(θ), where θ is the angle between the conductor and the magnetic field.
| 3. How does Fleming's Right Hand Rule differ from Fleming's Left Hand Rule? | |
Ans. Fleming's Right Hand Rule is used to determine the direction of induced current when a conductor moves through a magnetic field, indicating the principle of electromagnetic induction. In this rule, you align your thumb, index finger, and middle finger of your right hand perpendicular to each other, with the thumb pointing in the direction of motion of the conductor (relative to the magnetic field), the index finger pointing in the direction of the magnetic field (from North to South), and the middle finger will then point in the direction of the induced current. In contrast, Fleming's Left Hand Rule is used for motors, where the current is causing the movement, while the Right Hand Rule is used for generators, where motion is causing the current.
| 4. What is the formula to calculate the force on a current-carrying conductor in a magnetic field? | |
Ans. The formula to calculate the force (F) on a current-carrying conductor in a magnetic field is given by:
\[ F = BIL \sin(θ) \]
where:
- F is the force in Newtons (N),
- B is the magnetic field strength in Tesla (T),
- I is the current in Amperes (A),
- L is the length of the conductor in the magnetic field in meters (m),
- θ is the angle between the conductor and the magnetic field direction. The force is maximized when θ is 90 degrees (sin(90) = 1).
| 5. Can you provide an example of a practical application of the force on a current-carrying conductor in a magnetic field? | |
Ans. A practical application of the force on a current-carrying conductor in a magnetic field is found in electric motors. In an electric motor, current flows through coils of wire placed within a magnetic field. According to Fleming's Left Hand Rule, the interaction between the current and the magnetic field generates a force that causes the rotor to turn. This rotational motion is harnessed to perform work, such as turning the blades of a fan or powering a vehicle. The principles of electromagnetism are fundamental to the operation of various devices, including fans, pumps, and many household appliances.
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