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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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