Chapter 30
Problem 10
A single piece of wire is bent so that it includes a circular loop of radius a, as shown in
Fig. 3048. A current I flows in the direction shown. Find an expression for the magnetic
field at the center of the loop.
To solve this problem you will either need to use the equations for the magnetic field of a
current loop and a long straight wire, or you will need to derive those equations from the
BiotSavart law. Using the right hand rule, you can see that the magnetic field from the
loop and from the wire will both be out of the page. The equations for a loop and for a
long wire are given by 303 and 305 respectively.
2
/
3
2
2
2
0
)
(
2
a
x
Ia
B
loop
+
=
µ
is the equation for a loop and is derived on page 773. x is the distance from the center of
the loop, which is just 0 in our case because the loop is in the plane of the page. a is the
radius of the loop.
y
I
B
line
π
µ
2
0
=
is the equation for a line and is derived on page 776. y is the distance from the wire which
in our case also happens to be a, the radius of the loop. Since both fields point out of the
page, we can add them as scalars.
a
I
B
a
I
a
I
B
a
I
a
Ia
B
B
B
B
total
total
total
line
loop
total
π
π
µ
π
µ
µ
π
µ
µ
2
)
1
(
2
2
2
)
0
(
2
0
0
0
0
2
/
3
2
2
2
0
+
=
+
=
+
+
=
+
=
Problem 15
Part of a long wire is bent into a semicircle of radius a, as shown in Fig. 3050. A current
I flows in the direction shown. Use the BiotSavart law to find the magnetic field at the
center of the semicircle (point P).
The BiotSavart law is given by
∫
×
=
2
0
4
ˆ
r
r
l
Id
B
π
µ
v
v
dl is the vector along a given section of the current. The dl along the straight portion of
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 Spring '09
 SINHA
 Current, Magnetic Field, Righthand rule

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