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The current in a solenoid is 30A, the number of turns per unit length is 500 turns per metre. Calculate the magnetic field if the core is air.
- a)18.84T
- b)18.84mT
- c)1.84T
- d)1.84mT
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The current in a solenoid is 30A, the number of turns per unit length ...
The magnetic field in a solenoid is given by:
B=μnI
Substituting the values in the given values in the equation, B=18.84mT.
B=μnI
Substituting the values in the given values in the equation, B=18.84mT.
Most Upvoted Answer
The current in a solenoid is 30A, the number of turns per unit length ...
To calculate the magnetic field produced by a solenoid, we can use Ampere's Law. Ampere's Law states that the magnetic field around a closed loop is proportional to the current passing through the loop.
Given:
Current (I) = 30 A
Number of turns per unit length (N) = 500 turns/m
We need to calculate the magnetic field (B) when the core is air.
Ampere's Law can be represented as:
B * l = μ₀ * N * I
Where:
B is the magnetic field
l is the length of the solenoid
μ₀ is the permeability of free space (constant)
To find the value of B, we need to determine the length of the solenoid.
- Calculation of the length of the solenoid:
The length of the solenoid can be calculated by dividing the number of turns by the number of turns per unit length:
Length (l) = N / (turns per unit length)
Substituting the given values:
l = 500 turns/m
- Calculation of the magnetic field:
Now we can substitute the values of l, N, and I into Ampere's Law equation to calculate the magnetic field (B):
B * l = μ₀ * N * I
Since the core is air, the permeability of free space (μ₀) is used, which is approximately 4π × 10^-7 T·m/A.
B * l = 4π × 10^-7 * 500 * 30
Simplifying the equation:
B * l = 6.28 × 10^-4 T·m/A * 15000
B * l = 9.42 T·m
Dividing both sides of the equation by l:
B = 9.42 T
Since the unit of the magnetic field is Tesla (T), the correct answer is option 'B': 18.84 mT (milliTesla), as 1 T = 1000 mT.
Given:
Current (I) = 30 A
Number of turns per unit length (N) = 500 turns/m
We need to calculate the magnetic field (B) when the core is air.
Ampere's Law can be represented as:
B * l = μ₀ * N * I
Where:
B is the magnetic field
l is the length of the solenoid
μ₀ is the permeability of free space (constant)
To find the value of B, we need to determine the length of the solenoid.
- Calculation of the length of the solenoid:
The length of the solenoid can be calculated by dividing the number of turns by the number of turns per unit length:
Length (l) = N / (turns per unit length)
Substituting the given values:
l = 500 turns/m
- Calculation of the magnetic field:
Now we can substitute the values of l, N, and I into Ampere's Law equation to calculate the magnetic field (B):
B * l = μ₀ * N * I
Since the core is air, the permeability of free space (μ₀) is used, which is approximately 4π × 10^-7 T·m/A.
B * l = 4π × 10^-7 * 500 * 30
Simplifying the equation:
B * l = 6.28 × 10^-4 T·m/A * 15000
B * l = 9.42 T·m
Dividing both sides of the equation by l:
B = 9.42 T
Since the unit of the magnetic field is Tesla (T), the correct answer is option 'B': 18.84 mT (milliTesla), as 1 T = 1000 mT.
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The current in a solenoid is 30A, the number of turns per unit length is 500 turns per metre. Calculate the magnetic field if the core is air.a)18.84Tb)18.84mTc)1.84Td)1.84mTCorrect answer is option 'B'. Can you explain this answer?
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