Concept explainers
(a)
The current in the coil
(a)
Answer to Problem 54P
The current in the coil has a value of
Explanation of Solution
Write the equation for the magnetic field at the center of the coil.
Here,
Conclusion:
Substitute
Therefore, a current of
(b)
The rate of change of magnetic field
(b)
Answer to Problem 54P
The rate of change of magnetic field is
Explanation of Solution
Write the equation for the magnetic field along the axis of the coil at a distance
Here,
Differentiate the left hand side and the right hand side of the equation with respect to time
Conclusion:
Substitute
Therefore, the rate of change of magnetic field is
(c)
The distance from the coil at which the metals experience a magnetic field
(c)
Answer to Problem 54P
The metals or devices experience a magnetic field at a distance of
Explanation of Solution
Rewrite equation (II) to find the equation for
Conclusion:
Substitute
Therefore, the metals or devices experience a magnetic field at a distance of
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Chapter 23 Solutions
Principles of Physics: A Calculus-Based Text
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- Figure CQ19.7 shows a coaxial cable carrying current I in its inner conductor and a return current of the same magnitude in the opposite direction in the outer conductor. The magnetic field strength at r = r0 is Find the ratio B/B0, at (a) r = 2r0 and (b) r = 4r0. Figure CQ19.7arrow_forwardA rectangular coil consists of N = 100 closely wrapped turns and has dimensions a = 0.400 m and b = 0.300 m. The coil is hinged along the y axis, and its plane makes an angle = 30.0 with the x axis (Fig. P22.25). (a) What is the magnitude of the torque exerted on the coil by a uniform magnetic field B = 0.800 T directed in the positive x direction when the current is I = 1.20 A in the direction shown? (b) What is the expected direction of rotation of the coil? Figure P22.25arrow_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_forward
- The accompanying figure shows a cross-section of a long, hollow, cylindrical conductor of inner radius r1= 3.0 cm and outer radius r2= 5.0 cm. A 50-A current distributed uniformly over the cross-section flows into the page. Calculate the magnetic field at r = 2.0 cm. r = 4.0 cm. and r = 6.0 cm.arrow_forwardWithin 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_forward
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