Concept explainers
(a)
Find the magnitude and direction of the magnetic field due to the two loops at the origin.
(a)
Answer to Problem 29PQ
The direction of the magnetic field is out of the page and magnitude of magnetic field is
Explanation of Solution
Assume that magnetic field due to smaller loop is
Write the expression for magnetic field due to smaller loop as.
Here,
Write the expression for magnetic field due to larger loop as.
Here,
The direction of the magnetic field is outward.
Write the expression for net magnetic field as.
Substitute
Rearrange the above equation as.
Conclusion:
Substitute
Thus the direction of the magnetic field is out of the page and magnitude of magnetic field is
(b)
Determine the radius
(b)
Answer to Problem 29PQ
The magnetic field at the origin to be zero for
Explanation of Solution
When
Write the expression for the magnetic field at the origin to be zero as.
Rearrange the above equation as.
Rearrange the above equation as.
Here,
Conclusion:
Substitute
Thus, the magnetic field at the origin to be zero for
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Chapter 30 Solutions
Physics For Scientists And Engineers: Foundations And Connections
- 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 P30.83arrow_forwardA circular coil 15.0 cm in radius and composed of 145 tightly wound turns carries a current of 2.50 A in the counterclockwise direction, where the plane of the coil makes an angle of 15.0 with the y axis (Fig. P30.73). The coil is free to rotate about the z axis and is placed in a region with a uniform magnetic field given by B=1.35jT. a. What is the magnitude of the magnetic torque on the coil? b. In what direction will the coil rotate? FIGURE P30.73arrow_forwardFigure P30.10 shows a circular current-carrying wire. Using the coordinate system indicated (with the z axis out of the page), state the direction of the magnetic field at points A and B.arrow_forward
- For both sketches in Figure P30.56, there is a 3.54-A current, a magnetic field strength B 0.650 T. and the angle is 32.0. Find the magnetic force per unit length (magnitude and direction) exerted on the current-carrying conductor in both cases.arrow_forwardA wire is bent in the form of a square loop with sides of length L (Fig. P30.24). If a steady current I flows in the loop, determine the magnitude of the magnetic field at point P in the center of the square. FIGURE P30.24arrow_forwardA metal rod of mass m slides without friction along two parallel horizontal rails, separated by a distance and connected by a resistor R, as shown in Figure P30.13. A uniform vertical magnetic field of magnitude B is applied perpendicular to the plane of the paper. The applied force shown in the figure acts only for a moment, to give the rod a speed v. In terms of m, , R, B, and v, find the distance the rod will then slide as it coasts to a stop. Figure P30.13arrow_forward
- A toroid has a major radius R and a minor radius r and is tightly wound with N turns of wire on a hollow cardboard torus. Figure P31.6 shows half of this toroid, allowing us to see its cross section. If R r, the magnetic field in the region enclosed by the wire is essentially the same as the magnetic field of a solenoid that has been bent into a large circle of radius R. Modeling the field as the uniform field of a long solenoid, show that the inductance of such a toroid is approximately L=120N2r2R Figure P31.6arrow_forwardTwo long, straight wires carry the same current as shown in Figure P30.22. One wire is parallel to the z axis and the other wire is parallel to the x axis as shown. Find an expression for the magnetic field at the origin.arrow_forward
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