Biot-Savart Law: Circular Current Loop
A constant current I flows counterclockwise (viewed from above) in a circular loop of radius 'a'. What is the magnetic field at a point P that is a distance 'z' above the symmetry axis of the circular loop?
QUESTIONS
(Score is number right minus number wrong.)
A right-hand rule (thumb along the current direction) says that the resultant magnetic field at point P from the full current loop will be in the the
x-direction.
y-direction.
z-direction.
s-direction.
phi-direction.
For purposes of the integration of Equation (2), the Cartesian unit vectors (x,y,z) can always be treated as constants and brought outside the integral.
True
False
For purposes of the integration of Equation (2), the cylindrical unit vectors (s,phi,z) can equally well always be treated as constants and brought outside the integral.
True
False
Put the pieces of the integral together...
The vector position of the source point is given by,
Equation (6a)
Equation (6b)
Equation (6c)
Equation (6d)
Equation (6e)
Equation (6f)
The vector position of the field point is given by,
Equation (6a)
Equation (6b)
Equation (6c)
Equation (6d)
Equation (6e)
Equation (6f)
The magnitude of 'wavy r' is given by,
Equation (6a)
Equation (6b)
Equation (6c)
Equation (6d)
Equation (6e)
Equation (6f)
Since 'z' and 'a' are fixed (constants in the integration), we can bring 'wavy r' out of the integral and rewrite the integral as Equation (8).
True
False
The vector 'wavy r' is given by,
Equation (6a)
Equation (6b)
Equation (6c)
Equation (6d)
Equation (6e)
Equation (6f)
The unit 'wavy r' vector is given by Equation (6b).
True
False
The vector integration step (dl) is given by
Equation (6a)
Equation (6b)
Equation (6c)
Equation (6d)
Equation (6e)
Equation (6f)
Equation (7) is correct.
True
False
We can ignore any x or y components that appear in Equation (7) because the integrals for those components must vanish because of the symmetry of the problem.
True
False
The Biot-Savart integral in this problem simplifies miraculously to Equation (9).
True
False
EQUATIONS
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