Concept explainers
The required current in the top wire in the given figure to produce a field of zero at the point equidistant from the wires, provided currents in the bottom two wires are both 10.0 A into the page.
Answer to Problem 71PE
Explanation of Solution
Given:
Current carrying wire is placed at the vertices of an equilateral triangle of side 10.0 cm=
Formula used:
Magnetic field due to a long current carrying wire at perpendicular distance
Where
Calculation:
Label the wires at the vertices of triangle as P, Q and R.The equidistant point from all the three wires is centroid of the triangle. Let call the centroid point as O.
The perpendicular distance from the three wires to centroid of the triangle is
Let the current in P wire be
(Note the value of
Direction of fields at the centroid is shown by blue arrow in the figure below.
The resultant of vector
Now the net magnetic field at the centroid is
We want zero field at centroid. So,
Or
We are getting negative sign because what we have assumed the direction of current in wire P is not right to get zero field at centroid. So the new direction of current in top wire is to be into the page and its magnitude is
Conclusion:
Current in the top wire to produce a field of zero at the point equidistant from the wires is
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Chapter 22 Solutions
COLLEGE PHYSICS
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