Concept explainers
(a)
The sketch of the magnetic field pattern in the
(a)
Answer to Problem 72CP
The sketch of the magnetic field pattern in the
Explanation of Solution
The sketch of the magnetic field pattern in the
Figure-(1)
The current in the infinitely long wires are in the negative
(b)
The value of the magnetic field at the origin.
(b)
Answer to Problem 72CP
The value of the magnetic field at the origin is zero.
Explanation of Solution
There is symmetry in the loop, so the contribution of each wire to the magnetic field at the origin will be same in magnitude but opposite in the direction. So the net magnetic field at the origin will be zero.
Therefore, the value of the magnetic field at the origin is zero.
(c)
The value of the magnetic field at
(c)
Answer to Problem 72CP
The value of the magnetic field at
Explanation of Solution
Write the expression for the magnetic field.
Here,
Conclusion:
Substitute
Therefore, the value of the magnetic field at
(d)
The magnetic field at points along the
(d)
Answer to Problem 72CP
The magnetic field at points along the
Explanation of Solution
Write the equation of the magnetic field in
So, this can be written as,
Conclusion:
Substitute
Therefore, the magnetic field at points along the
(e)
The distance along the positive
(e)
Answer to Problem 72CP
The distance along the positive
Explanation of Solution
Write the condition the maximum magnetic field.
Substitute
Conclusion:
Substitute
Therefore, the distance along the positive
(f)
The maximum value of the magnetic field.
(f)
Answer to Problem 72CP
The maximum value of the magnetic field is
Explanation of Solution
Conclusion:
Substitute
Therefore, the maximum value of the 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 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 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_forward
- Figure 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_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_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_forwardIn Figure P30.38, the rolling axle, 1.50 m long, is pushed along horizontal rails at a constant speed v = 3.00 m/s. A resistor R = 0.400 is connected to the rails at points a and b, directly opposite each other. The wheels make good electrical contact with the rails, so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R. A uniform magnetic field B = 0.080 0 T is vertically downward. (a) Find the induced current I in the resistor. (b) What horizontal force F is required to keep the axle rolling at constant speed? (c) Which end of the resistor, a or b, is at the higher electric potential? (d) What If? After the axle rolls past the resistor, does the current in R reverse direction? Explain your answer. Figure P30.38arrow_forwardFigure P32.21 shows a circular conducting loop with a 5.00-cm radius and a total resistance of 1.30 placed within a uniform magnetic field pointing into the page. a. What is the rate at which the magnetic field is changing if a counterclockwise current I = 4.60 102 A is induced in the loop? b. Is the induced current caused by an increase or a decrease in the magnetic field with time?arrow_forward
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