# Magnetic fields, Ampere's law, current

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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?

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##### Solution Summary

Magnetic fields, Ampere's law and current are examined.

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Please see the attached file.

The magnetic field due a long current carrying wire at a distance r from it is given by using Ampere's law as

The direction of the magnetic field at a point is given by the right hand rule.

Now here the field at point A midway between the wires due to the left wire carrying current I will be

According to right hand rule, as the direction of this current is upward at A the field will be into the paper, means negative z direction and hence

----------------- (1)

The field at A due to the wire carrying current I on right will be

According to right hand rule, as the direction of this current is downward at A the field will be again into the paper means negative z direction and hence

------------------- (2)

Hence the total field at A is given by

Hence the field midway is 4*10-5 T and it points into the plane of the paper.

Now the field at point B due to the left wire carrying current I will be

According to right hand rule, as the direction of this current is upward at B the field will be out of the paper, means positive z direction and hence

----------------- (3)

The field at B due to the wire carrying current I on right will be

According to right hand rule, as the direction of this current is downward at B the field will be into the paper ...

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