The figure below shows very long current-carrying wires. Using the coordinate system indicated (with the z axis out of the page), state the direction of the magnetic field at point P in each case.
www.webassign.net/katzpse1/30-p-009.png
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https://www.webassign.net/katzpse1/30-p-009.png
To determine the direction of the magnetic field at point P in each case, you can use the right-hand rule. Here's how you can apply the right-hand rule to find the direction of the magnetic field:
1. Extend your right hand and align your thumb with the direction of the current flow in the wire.
2. Wrap your fingers around the wire in the direction of the circular magnetic field lines.
3. The direction your fingers curl around the wire represents the direction of the magnetic field.
Now, let's apply the right-hand rule to the given figure:
Case 1:
Based on the given figure, the current in wire A is going into the page, and the current in wire B is coming out of the page.
To find the direction of the magnetic field at point P, imagine gripping wire A with your right hand, so that your thumb is pointing into the page (opposite to the current direction). Now, curl your fingers around the wire. The direction in which your fingers curl represents the direction of the magnetic field at point P. In this case, your fingers will curl in a clockwise direction.
Therefore, the direction of the magnetic field at point P is clockwise.
Case 2:
In this case, the currents in both wire A and wire B are going into the page.
To find the direction of the magnetic field at point P, imagine gripping either wire A or wire B with your right hand, so that your thumb is pointing into the page (opposite to the current direction). Now, curl your fingers around the wire. The direction in which your fingers curl represents the direction of the magnetic field at point P. In this case, your fingers will curl in a clockwise direction.
Therefore, the direction of the magnetic field at point P is clockwise.
To visualize the right-hand rule and the direction of the magnetic field, you can refer to the provided figure.