Concept explainers
Two long, straight, parallel wires carry current as shown in Figure P30.18. If the currents are equal, find an expression for the magnetic field at point C. Use the indicated coordinate system to write your answer in component form.
FIGURE P30.18
Find the expression for the magnetic field at point C in component form
Answer to Problem 20PQ
The expression for net magnetic field at point C is
Explanation of Solution
Redraw the figure P30.19 as shown below:
Write the general expression for magnetic field due to wire as.
Here,
The direction of the magnetic field at a point due to a current carrying wire is given by the right hand palm rule.
According to this rule, the thumb of the right hand faces in the direction of the current in the wire, the fingers face towards the point at which magnetic field is to be calculated then the palm faces in the direction of the magnetic field.
The current flowing in the wires is same and the point is at the equal distances from both the wire. Therefore, the vertical components of the magnetic fields will be same for both wires and they will cancel out each other.
Write the expression for the net magnetic field at point C refers to figure (a) above as.
Here,
Apply Pythagoras theorem in triangle
Simplify above equation as.
Apply Pythagoras theorem in triangle
Simplify above equation as.
The net magnetic field due to the two wires is in the positive X-direction. The components of the field in the X-direction are calculated as below.
Substitute
Here,
Substitute
Here,
Write the expression for the value of
Substitute
Substitute
Conclusion:
Substitute
Thus, the expression for net magnetic field at point C is
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Chapter 30 Solutions
Student Solutions Manual For Katz's Physics For Scientists And Engineers: Foundations And Connections, Volume 1
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