Concept explainers
Two infinitely long current-carrying wires run parallel in the xy plane and are each a distance d = 11.0 cm from the y axis (Fig. P30.83). The current in both wires is I = 5.00 A in the negative y direction.
- a. Draw a sketch of the magnetic field pattern in the xz plane due to the two wires. What is the magnitude of the magnetic field due to the two wires
- b. at the origin and
- c. as a function of z along the z axis, at x = y = 0?
FIGURE P30.83
(a)
The sketch of the magnetic field pattern in the x-z plane due to the two wires.
Answer to Problem 83PQ
The direction of the magnetic field pattern in x-z plane is shown in figure (a).
Explanation of Solution
The direction of the magnetic field for a current carrying wire is given by the Right Hand Palm rule.
According to the right hand palm rule, the thumb of the right hand points in the direction of the current flowing in the wire, the fingers point along the point at which the magnetic field is to be calculated then the palm faces towards the direction of the magnetic field.
Here, the direction of magnetic field due to both wires is in anticlockwise direction.
Conclusion:
Thus, the direction of the magnetic field pattern in x-z plane is shown in figure (a).
(b)
The magnitude of the magnetic field due to the two wires at the origin.
Answer to Problem 83PQ
The magnitude of the magnetic field due to the two wires at the origin in zero.
Explanation of Solution
The direction of the magnetic field due to first wire and the second wire is shown as.
Write the expression forthe magnetic field due to first wire.
Here
Write the expression for the magnetic field due to second wire.
Here
Write the expression for the net magnetic field at the origin as.
Here,
Conclusion:
Substitute
Hence, the net magnetic field at the origin will be zero.
(c)
The magnitude of the magnetic field due to two wire as a function of z along the z-axis.
Answer to Problem 83PQ
The magnetic field due to two wires as a function of z along the Z-axis is
Explanation of Solution
The direction of the magnetic field for a current carrying wire is given by the Right Hand Palm rule.
The magnetic field due to both wires will be in negative X-direction at some point z above the origin.
Write the expression for the magnetic field due to first wire as.
Here,
The net magnetic field due to the second wire is same as that of the magnetic field due to the first wire.
Write the expression for the magnetic field due to second wire as.
Here,
The distance of the point along the Z-axis from the wire is given by the Pythagoras theorem.
Write the expression for the distance
Here,
Write the expression for the angle made by the position vector with the horizontal as.
Substitute
Write the expression for the net magnetic field as.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Thus, the magnetic field due to two wires as a function of z along the Z-axis is
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