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A 90 cm long solenoid has six layers of windings of 450 turns each. If the diameter of solenoid is 2.2 cm and current carried is 6A, then the magnitude of magnetic field inside the solenoid, near its centre is
  • a)
    50π G
  • b)
    60π G
  • c)
    72π G
  • d)
    80π G
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A 90 cm long solenoid has six layers of windings of 450 turns each. If...
For six layers of windings the total number of turns = 6 x 450 = 2700
Now number of turns per unit length 

Then the field in side the solenoid near the centre 
B = μ0nI = 4π x 10-7 x 3000 x 6  = 72π x 10-4 T = 72πG
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Most Upvoted Answer
A 90 cm long solenoid has six layers of windings of 450 turns each. If...
The magnetic field inside a solenoid can be calculated using the formula:

B = μ₀ * n * I

where B is the magnetic field, μ₀ is the permeability of free space (4π × 10⁻⁷ T m/A), n is the number of turns per unit length, and I is the current.

To find n, we need to calculate the number of turns per unit length. The length of the solenoid is given as 90 cm, and it has six layers of windings with 450 turns each. Therefore, the total number of turns is:

Total number of turns = number of turns per layer * number of layers
= 450 turns/layer * 6 layers
= 2700 turns

The length per turn can be calculated by dividing the total length of the solenoid by the total number of turns:

Length per turn = 90 cm / 2700 turns
= 0.033 cm/turn

To find n, we need to convert the length per turn to meters:

Length per turn = 0.033 cm/turn * (1 m/100 cm)
= 0.00033 m/turn

Now we can calculate n:

n = 1 / length per turn
= 1 / 0.00033 m/turn
= 3030.3 turns/m

Plugging in the values for μ₀ (4π × 10⁻⁷ T m/A), n (3030.3 turns/m), and I (6 A) into the formula for magnetic field, we get:

B = μ₀ * n * I
= (4π × 10⁻⁷ T m/A) * (3030.3 turns/m) * (6 A)
≈ 0.072 T

Therefore, the magnitude of the magnetic field inside the solenoid, near its center, is approximately 0.072 T.
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A 90 cm long solenoid has six layers of windings of 450 turns each. If the diameter of solenoid is 2.2 cm and current carried is 6A, then the magnitude of magnetic field inside the solenoid, near its centre isa)50π Gb)60π Gc)72π Gd)80π GCorrect answer is option 'C'. Can you explain this answer?
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