# Ampere's Law: Magnetic field from a wire

Consider a straight section of wire of length L which carries a current I, as shown below. Show that the magnetic field at a point P a distance R from the wire along its perpendicular bisector is B = (muI/2piR) * L/(L^2 + 4R^2)^1/2

^

: :

: :

L/2 : I :

:

: R

:-------------------->P

:

L/2 :

:

:

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#### Solution Preview

See the attached file for full calculations.

:C(by letting dx be at C)

:

:L/2

:

:.............................P

O R

The angle (pi-theta) ...

#### Solution Summary

With complete formulas and calculations, the problem is solved.

Magnetic fields, Ampere's law, current

1. Two wires shown are separated by d=10 cm and carry currents of I=5.0 A in opposite directions. Find the magnitude and direction of the net magnetic field at:

i) A point midway between the wires.

ii) A point 2s=20 cm to the left of the wire on the left.

2. Using Ampere's law, erive the magnetic field produced at a point:

i) r inside a wire of radius R.

ii) r outside the wire of radius R.

3. A conducting bar of mass m, length l, makes a circuit with resistor R. The bar moves to the left without friction in a horizontal plane, moving on parallel conducting rails as shown in the figure below. A constant magnetic field B is directed perpendicular, in the outward direction, to the plane of the page.

a) At what constant speed should the bar move to priduce an 8.5 mA current in the resistor?

b) What is the direction of the current?

c) At what rate is energy delivered to the resistor?

d) Where is the energy coming that is delivered to the resistor?