Concept explainers
(a)
To draw: The magnetic field pattern in the
(a)
Answer to Problem 30.72CP
The magnetic field pattern in the
Figure (1)
Explanation of Solution
Given info: The amount of current flow in infinitely long wire is
The magnetic field pattern in the
Figure (1)
From the right hand thumb rule, when the thumb is directed towards the direction of current, the curled fingers show the direction of magnetic field.
(b)
The value of magnetic field at origin.
(b)
Answer to Problem 30.72CP
The value of magnetic field at origin is
Explanation of Solution
Given info: The amount of current flow in infinitely long wire is
The direction of magnetic field due to current carry wire is shown below.
Figure (2)
Write the expression for the magnetic field due to current carrying wire.
Here,
From the given figure,
Substitute
The magnetic field component
The resultant magnetic field along
Substitute
From the figure (2),
Substitute
Conclusion:
Therefore, the value of magnetic field at origin is
(c)
The value of magnetic field at
(c)
Answer to Problem 30.72CP
The value of magnetic field at
Explanation of Solution
Given info: The amount of current flow in infinitely long wire is
From the equation (3), the expression for magnetic field is,
The value of magnetic field at
Conclusion:
Therefore, the value of magnetic field at
(d)
The magnetic field at points along the
(d)
Answer to Problem 30.72CP
The magnetic field at points along the
Explanation of Solution
Given info: The amount of current flow in infinitely long wire is
From the calculated value in part (b), the magnetic field at points along the
Conclusion:
Therefore, the magnetic field at points along the
(e)
The distance along the positive
(e)
Answer to Problem 30.72CP
The magnetic field is maximum at
Explanation of Solution
Given info: The amount of current flow in infinitely long wire is
From the calculated value in part (b), the magnetic field at points along the
For maximum value of
Substitute
Substitute
Conclusion:
Therefore, the magnetic field is maximum at
(f)
The maximum value of magnetic field.
(f)
Explanation of Solution
Given info: The amount of current flow in infinitely long wire is
From the calculated value in part (b), the magnetic field at points along the
Substitute
Substitute
Simplify further,
Conclusion:
Therefore, the maximum value of magnetic field is
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Chapter 30 Solutions
EBK PHYSICS:F/SCI.+ENGRS.,TECH.UPDATED
- 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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