**Magnetic Field Due to a Current-Carrying Loop**In this problem, a closed loop carries a current \( i = 326 \, \text{mA} \). The loop consists of two radial straight wires and two concentric circular arcs with radii of 1.76 m and 4.04 m. The angle \( \theta \) is 1.31 radians. We aim to determine the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at the center of curvature, point P.**Diagram Analysis:**The diagram depicts two concentric circular arcs connected by radial straight wires. The current flows uniformly through the loop starting from one radial wire, moving through the arcs, and returning through the other wire. The two arcs represent parts of circles with a shared center at point P.- The wider arc has a radius of 4.04 m.- The smaller arc has a radius of 1.76 m.- Point P is located at the center of the arcs.- The current flows in the direction indicated by the arrow on the larger arc, making an angle \( \theta = 1.31 \) radians at point P.**Questions:**(a) **Magnitude:** Calculate the magnetic field magnitude at point P using the Biot-Savart law or Ampère's Law, considering vector contributions from both arcs.(b) **Direction:** Determine whether the net magnetic field at point P is directed into or out of the page based on the right-hand rule.**Note:** Use the correct number of significant digits, with a tolerance of \(\pm 2\%\) for precision.

radius, r1 = 1.76 m radius, r2 = 4.04 m i = 326 mA Angle = 1.31 rad

In the figure, a closed loop carries current i = 326 mA. The loop consists of two radial straight wires and two concentric circular arcs of radii 1.76 m and 4.04 m. The angle 0 is 1.31 rad. What are the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at the center of curvature P?

In the figure, a closed loop carries current i = 326 mA. The loop consists of two radial straight wires and two concentric circular arcs of radii 1.76 m and 4.04 m. The angle 0 is 1.31 rad. What are the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at the center of curvature P?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Magnetic Field Of Coaxial Cable

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

Question

**Magnetic Field Due to a Current-Carrying Loop**

In this problem, a closed loop carries a current \( i = 326 \, \text{mA} \). The loop consists of two radial straight wires and two concentric circular arcs with radii of 1.76 m and 4.04 m. The angle \( \theta \) is 1.31 radians. We aim to determine the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at the center of curvature, point P.

**Diagram Analysis:**

The diagram depicts two concentric circular arcs connected by radial straight wires. The current flows uniformly through the loop starting from one radial wire, moving through the arcs, and returning through the other wire. The two arcs represent parts of circles with a shared center at point P.

- The wider arc has a radius of 4.04 m.
- The smaller arc has a radius of 1.76 m.
- Point P is located at the center of the arcs.
- The current flows in the direction indicated by the arrow on the larger arc, making an angle \( \theta = 1.31 \) radians at point P.

**Questions:**

(a) **Magnitude:** Calculate the magnetic field magnitude at point P using the Biot-Savart law or Ampère's Law, considering vector contributions from both arcs.

(b) **Direction:** Determine whether the net magnetic field at point P is directed into or out of the page based on the right-hand rule.

**Note:** Use the correct number of significant digits, with a tolerance of \(\pm 2\%\) for precision.

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