Respuesta :
Given Information:
Length of wire = 132 cm = 1.32 m
Magnetic field = B = 1 T
Current = 2.2 A
Required Information:
(a) Torque = τ = ?
(b) Number of turns = N = ?
Answer:
(a) Torque = 0.305 N.m
(b) Number of turns = 1
Explanation:
(a) The current carrying circular loop of wire will experience a torque given by
τ = NIABsin(θ) eq. 1
Where N is the number of turns, I is the current in circular loop, A is the area of circular loop, B is the magnetic field and θ is angle between B and circular loop.
We know that area of circular loop is given by
A = πr²
where radius can be written as
r = L/2πN
So the area becomes
A = π(L/2πN)²
A = πL²/4π²N²
A = L²/4πN²
Substitute A into eq. 1
τ = NI(L²/4πN²)Bsin(θ)
τ = IL²Bsin(θ)/4πN
The maximum toque occurs when θ is 90°
τ = IL²Bsin(90)/4πN
τ = IL²B/4πN
torque will be maximum for N = 1
τ = (2.2*1.32²*1)/4π*1
τ = 0.305 N.m
(b) The required number of turns for maximum torque is
N = IL²B/4πτ
N = 2.2*1.32²*1)/4π*0.305
N = 1 turn
Maximum torque and Number of coil for maximum torque 3,046.428 and 1.
Given information about question:
Length of wire = 132 cm
Current carries = 2.2 A
Intensity = 1T
Find:
Maximum torque
Number of coil for maximum torque
Computation:
We know that
2πr = 132
So,
r = 21 cm
A = πr²
A = (3.14)(21)²
A = 1,384.74 cm²
T(max) = IAB
T(max) = (1)(1,384.74)(2.2)
T(max) = 3,046.428
Number of coil for maximum torque = T(max) / IAB
Number of coil for maximum torque = 3,046.428 / 3,046.428
Number of coil for maximum torque = 1 coil
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