Concept explainers
(a)
The magnitude and the direction of the net magnetic field at the mid way between the wires.
(a)
Answer to Problem 19P
The magnitude of the net magnetic field is
Explanation of Solution
Write the expression to obtain the magnetic field along the conductor.
Here,
Write the expression to obtain the magnetic field due to the wire
Here,
Write the expression to obtain the magnetic field due to the wire
Here,
Write the expression to obtain the net magnetic field at the mid way between the wires.
Here,
Substitute
Further substitute
Conclusion:
Substitute
Therefore, the magnitude of the net magnetic field is
(b)
The magnitude and the direction of the net magnetic field at point
(b)
Answer to Problem 19P
The magnitude of the net magnetic field is
Explanation of Solution
Write the expression to obtain the magnetic field due to the wire
Here,
Write the expression to obtain the magnetic field due to the wire
Here,
Write the expression to obtain the net magnetic field at the mid way between the wires.
Here,
Substitute
Further substitute
Conclusion:
Substitute
Therefore, the magnitude of the net magnetic field is
(c)
The magnitude and the direction of the net magnetic field at point
(c)
Answer to Problem 19P
The magnitude of the net magnetic field is
Explanation of Solution
Write the expression to obtain the magnetic field due to the wire
Here,
Write the expression to obtain the magnetic field due to the wire
Here,
Write the expression to obtain the net magnetic field at the mid way between the wires.
Here,
Substitute
Further substitute
Conclusion:
Substitute
Therefore, the magnitude of the net magnetic field is
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Chapter 30 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
- 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 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 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_forwardA 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_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
- Within the green dashed circle show in Figure P30.21, the magnetic field changes with time according to the expression B = 2.00t3 4.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.50 cm. When t = 2.00 s, calculate (a) the magnitude and (b) the direction of the force exerted on an electron located at point P, which is at a distance r = 5.00 cm from the center of the circular field region. (c) At what instant is this force equal to zero? Figure P30.21arrow_forwardA uniform magnetic field B=5.44104iT passes through a closed surface with a slanted top as shown in Figure P31.59. a. Given the dimensions and orientation of the closed surface shown, what is the magnetic flux through the slanted top of the surface? b. What is the net magnetic flux through the entire closed surface?arrow_forwardFor 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_forward
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