Exam II Solutions
PHY2054
Summer 2011
P. Kumar
1. Two wires each carry 10 A current in opposite direction and are 3.0 mm apart.
What is the
magnetic field at a point P,
25 cm away and in the plane of the wires.
The magnetic field is calculated
from B =
μ
0
I/(2
π
r).
The two wires give you fields at point P in the
opposite directions and the difference between them is the net magnetic field at point P.
If you
calculate the fields separately; let us do that for the nearest wire at a distance of 25.00 cm away for
which we get 8
μ
T.
Due to the wire 25.3 cm away, the field is
7.9051
μ
T.
Take the difference and that
would be the answer.
But you must calculate both to at least 4 decimal places. An easier thing to do
would be to carry the calculation algebraically all the way:
Which directly provides the answer
B = 94.86 nT.
A point could be made that with modern calculators,
this sort of care is quite unnecessary.
2. A straight stiff wire of length 1.00 m and mass 25 g is suspended in
a magnetic field B = 0.75 T.
How much current must flow in the
wire so that the wire is suspended with no tension in the springs?
It is clear that to counteract the force of gravity on the hanging wire, the
current must be from left to right.
=
0.327 A.
3. A long straight wire carries a current i
1
= 30 A and a rectangular loop carries
a current i
2
= 20 A.
Taking a = 1.00 cm, b = 8.00 cm and L = 30.00 cm,
what is the net force on the loop due to the wire i
1
?
Here the magnetic field due to the wire is into the plane of the paper and decreases
with distance from the wire.
The forces on the right and left branches of the loop
are outwards, to the right at the right wire and to the left at the left branch.
They
cancel even though their calculation must incorporate the distance dependence of the field.
At the top
and the bottom wires the field is constant, into the plane of the paper and the force is attractive for the
top wire and bigger since it is closer.
The net force on the loop is the difference between the top and
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 Summer '08
 Any
 Physics, Current, Magnetic Field

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