Transcript Electric Potential - McMaster Physics and Astronomy

More Examples of
Biot-Savart &
Ampère’s Law
Recall:
ds  ˆr
 r2
Biot-Savart Law:
μo I
B
4π
Ampere’s Law:
B

d
s


I
o

Quiz: A light, loose spiral spring carrying no current
is hung from a ceiling. When a switch is closed so
that a circuit exists in the spring, do the coils:
a) move farther apart
b) move closer together
c) do not move at all
Example 1: A very long straight wire carries current I. In
the middle of the wire a right-angle bend is made. The bend
forms an arc of a circle of radius r, as shown below. Determine
the magnetic field at the center of the arc.
Solution
Example 2: A closed current path shaped as shown below
produces a magnetic field at P. If the arc subtends an angle
of 300 and the total length of the wire is 1.2m, what are the
magnitude and direction of the field produced at P if the
current in the loop is 3.0 A ?
300
P
Solution
Example 3: For the arrangement shown in the figure below,
the current in the long, straight wire has value I1=5 A and lies
in the plane of the rectangular loop, which carries a current
I2=10 A. The dimensions are a=0.15m, c=0.1m and L=0.45m.
Find the net force exerted on the rectangle by the magnetic
field of the straight current-carrying conductor.
I2
I1
c
a
L
Solution
Example 4: A long cylindrical conductor of radius R carries
a current I. The current density J, however, is not uniform
over the conductor but is a function of radius according to
J=br, where b is a constant.
Find an expression for the magnetic field B at:
a) r<R
b) r>R
Solution