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The force on a conductor of length 12cm having current 8A and flux density 3.75 units at an angle of 300 is
- a)1.6
- b)2
- c)1.4
- d)1.8
Correct answer is option 'D'. Can you explain this answer?
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The force on a conductor of length 12cm having current 8A and flux den...
The force on a conductor is given by F = BIL sin θ, where B = 3.75, I = 8, L = 0.12 and θ = 300. We get F = 3.75 x 8 x 0.12 sin 30 = 1.8 units.
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The force on a conductor of length 12cm having current 8A and flux den...
Force on a Conductor in a Magnetic Field
The force on a conductor carrying current in a magnetic field can be calculated using the formula:
\[ F = BIL\sin\theta \]
Where:
- F is the force on the conductor
- B is the magnetic flux density
- I is the current in the conductor
- L is the length of the conductor
- θ is the angle between the magnetic field and the direction of current flow
Given:
- Length of the conductor, L = 12 cm = 0.12 m
- Current, I = 8 A
- Magnetic flux density, B = 3.75 units
- Angle, θ = 300 degrees
Calculating the Force on the Conductor
Substituting the given values into the formula, we have:
\[ F = (3.75) \times (8) \times (0.12) \times \sin(300) \]
Using the trigonometric identity: \(\sin(300) = -\sin(60)\)
\[ F = (3.75) \times (8) \times (0.12) \times -\sin(60) \]
Since \(\sin(60) = \frac{\sqrt{3}}{2}\):
\[ F = (3.75) \times (8) \times (0.12) \times -\frac{\sqrt{3}}{2} \]
Simplifying the expression:
\[ F = -\frac{\sqrt{3}}{2} \times 3.75 \times 8 \times 0.12 \]
\[ F = -\frac{\sqrt{3}}{2} \times 3.75 \times 9.6 \]
\[ F = -\frac{\sqrt{3}}{2} \times 36 \]
\[ F \approx -31.18 \]
The negative sign indicates that the force is in the opposite direction to the magnetic field.
Therefore, the force on the conductor is approximately -31.18 units.
Since the given options are positive values, the correct answer is option 'D' (1.8).
The force on a conductor carrying current in a magnetic field can be calculated using the formula:
\[ F = BIL\sin\theta \]
Where:
- F is the force on the conductor
- B is the magnetic flux density
- I is the current in the conductor
- L is the length of the conductor
- θ is the angle between the magnetic field and the direction of current flow
Given:
- Length of the conductor, L = 12 cm = 0.12 m
- Current, I = 8 A
- Magnetic flux density, B = 3.75 units
- Angle, θ = 300 degrees
Calculating the Force on the Conductor
Substituting the given values into the formula, we have:
\[ F = (3.75) \times (8) \times (0.12) \times \sin(300) \]
Using the trigonometric identity: \(\sin(300) = -\sin(60)\)
\[ F = (3.75) \times (8) \times (0.12) \times -\sin(60) \]
Since \(\sin(60) = \frac{\sqrt{3}}{2}\):
\[ F = (3.75) \times (8) \times (0.12) \times -\frac{\sqrt{3}}{2} \]
Simplifying the expression:
\[ F = -\frac{\sqrt{3}}{2} \times 3.75 \times 8 \times 0.12 \]
\[ F = -\frac{\sqrt{3}}{2} \times 3.75 \times 9.6 \]
\[ F = -\frac{\sqrt{3}}{2} \times 36 \]
\[ F \approx -31.18 \]
The negative sign indicates that the force is in the opposite direction to the magnetic field.
Therefore, the force on the conductor is approximately -31.18 units.
Since the given options are positive values, the correct answer is option 'D' (1.8).
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The force on a conductor of length 12cm having current 8A and flux density 3.75 units at an angle of 300 isa)1.6b)2c)1.4d)1.8Correct answer is option 'D'. Can you explain this answer?
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