Part A – Pass Section Problem 1 A straight wire of length L has a current I running through it in the direction +æ, to the right of the page. L +y +x d (a) Draw a sketch of the magnetic field lines produced by the current. (b) Consider a point P that is a distance d from the length of wire, and equidistant from both ends. Der the expression for the magnetic field at the point P as a function of the distance d, explaining the m steps in your own words. Hint: consider first the magnetic field produced by an element of wire. You may find the following relat useful, dx 21 %3D 1 (a² + x²)3/2 ¯ a² Va² + l² (c) Show that when L» d, the magnetic field at point P approaches the field from an infinitely-long curre carrying wire.
Part A – Pass Section Problem 1 A straight wire of length L has a current I running through it in the direction +æ, to the right of the page. L +y +x d (a) Draw a sketch of the magnetic field lines produced by the current. (b) Consider a point P that is a distance d from the length of wire, and equidistant from both ends. Der the expression for the magnetic field at the point P as a function of the distance d, explaining the m steps in your own words. Hint: consider first the magnetic field produced by an element of wire. You may find the following relat useful, dx 21 %3D 1 (a² + x²)3/2 ¯ a² Va² + l² (c) Show that when L» d, the magnetic field at point P approaches the field from an infinitely-long curre carrying wire.
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Transcribed Image Text:Part A – Pass Section
Problem 1
A straight wire of length L has a current I running through it in the direction +x, to the right of the page.
L
+y
+x
P
(a) Draw a sketch of the magnetic field lines produced by the current.
(b) Consider a point P that is a distance d from the length of wire, and equidistant from both ends. Derive
the expression for the magnetic field at the point P as a function of the distance d, explaining the main
steps in your own words.
Hint: consider first the magnetic field produced by an element of wire. You may find the following relation
useful,
dr
21
J-i (a² + x²)3/2
a²Va² + l²
(c) Show that when L > d, the magnetic field at point P approaches the field from an infinitely-long current-
carrying wire.
(d) Two long current-carrying wires with weight per unit length 0.075 N/m are oriented along the r axis and
are vertically separated by a distance d = 3.0 mm. The top wire is fixed in position and a current passes
through it to the right (+æ), as in the diagram above. The bottom wire is free to move. We would like
to levitate the bottom wire in the magnetic field created by the top wire. To achieve this, what would be
the required:
(i) direction of the current in the bottom wire?
(ii) magnitude of the current, if this value is the same in the top and bottom wires.
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