Question:A magnetic field of 37.2 T has been achieved at the MIT Francis
Bitter National Magnetic...
Question
A magnetic field of 37.2 T has been achieved at the MIT Francis
Bitter National Magnetic...
A magnetic field of 37.2 T has been achieved at the MIT Francis
Bitter National Magnetic Laboratory. Find the current needed to
achieve such a field
a) 2.00 cm from a long straight wire
b) At the centre of a circular coil of radius 42.0 cm that has 100
turns
c) Near the center of a solenoid with radius 2.40 cm, length 32.0
cm and 40000 turns
The given problem can be solved by using the expression of magnetic field due to straight current carrying conductor, at the center of circular coil and near the center of solenoid.
To get the value of current, rearrange the expression of magnetic field due to straight current carrying conductor, at the center of circular coil and near the center of solenoid.
Fundamentals
The expression of magnetic field due to straight current carrying conductor can be expressed as follows,
B=2πlμ0i
Here, μ0=(4π×10−7T⋅m⋅A−1) , i is the current, l is the length of the conductor.
The expression of magnetic field at the center of circular of coil can be expressed as follows,
B=2rμ0Ni
Here, μ0=(4π×10−7T⋅m⋅A−1) , i is the current and r is the radius of circular coil.
The expression of magnetic field near the center of the solenoid can be expressed as follows,
B=lμ0Ni
Here, μ0=(4π×10−7T⋅m⋅A−1) , i is the current and l is the length of the solenoid.
(A)
The expression of magnetic field due to straight current carrying conductor can be expressed as follows,
B=2πlμ0i
Rearrange the expression to get the value of current.
i=μ0B(2πl)
Substitute 4π×10−7T⋅m⋅A−1 for μ0 , 37.2T for B and 2.00cm for l in the expression of current.