A straight wire segment lies on the x-axis and extends from x=-a to
x=0. It carries a constant current, I, directed along the positive
x-axis. Use the Biot-Savart law for this calculation.
I=8.00 A
a = 12.0 cm
(a) Choose an arbitrary point (x,y) in the first quadrant and
derive a formula for the magnetic field: B(x,y) due to the current
in the wire segment.
(b) Using Maple, plot the magnitude B(x,y) along the line
y = (0.0100)x+(0.0200 m)
in the range 0 � x � 0.0300 m.
In class, an expression for the magnetic field on the planar axis of
a semi-circular current-carrying loop was found to be
B
=
moIa2
4p
� �
p
0
dq
(a2+y2o+2ayosinq)3/2
^
z
+
moIayo
4p
� �
p
0
sinq dq
(a2+y2o+2ayo sinq)3/2
^
z
(a) Using the Biot-Savart law as was done in Physics III, show that
the magnetic field at the center of curvature of the semi-circular wire is
Bc=moI/4a
(b) Using the above integral expression, show that it reduces to the
same expression you found in part (a).
(c) Plot the integrands for a=0.100 m, yo=0.100 m, and
I=12.0 A in the interval 0 � q � p.
(d) Evaluate the two integrals for the numbers given in part (c) and
show that the total magnetic field is
B(yo=0.1 m)=1.06×10-5 T
The magnetic field inside a long, straight cylindrical wire carrying
a constant current is
B
=
� �
mo I
2pa2
� �
s
^
j
Calculate the current density, J, inside the wire.
A circular wire of radius a lies in the x-y plane and is centered
at the origin. The wire carries a constant current I in the
counter-clockwise direction. The magnetic field at point P on the z-axis
(as determined by the Biot-Savart Law) is
B(P)
=
moIa2
2(z2+a2)3/2
^
z
The existence of �Bz/�z is clearly seen from the
equation for B. The other two partial derivatives
�Bx/�x and �By/�y also exist even
though the field equation does not contain either Bx or By! Use the
divergence of B to find the other two derivatives. Comment on why
they must NOT be zero.
Text: 5.16.
File translated from
TEX
by
TTH,
version 3.85. On 10 Dec 2009, 17:07.