(a)
The magnetic flux through the top face of the cube
(a)
Answer to Problem 64PQ
The magnetic flux through the top face of the cube is
Explanation of Solution
Write the expression of the magnetic flux.
Here,
Write the expression for the normal area vector of the top face of the cube.
Here,
Conclusion:
Substitute
Substitute
Thus, the magnetic flux through the top face of the cube is
(b)
The total magnetic flux through all six faces of a cube.
(b)
Answer to Problem 64PQ
The net magnetic flux through all the six faces of the cube is
Explanation of Solution
Gauss’s law for magnetic states that the total magentic flux through a closed surface is equal to zero, i.e, all the line coming outside of the cube will ultimately go inside the body, becouse they from closed loops. Mathemeatically, it can be shown that the total magnetic flux is zero.
Write the expression for the net magnetic flux
Here,
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the net magnetic flux through all the six faces of the cube is
Want to see more full solutions like this?
Chapter 31 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- A toroid with an inner radius of 20 cm and an outer radius of 22 cm is tightly wound with one layer of wire that has a diameter of 0.25 mm. (a) How many turns are there on the toroid? (b) If the current through the toroid windings is 2.0 A, what is the strength of the magnetic field at the center of the toroid?arrow_forwardA uniform magnetic field of magnitude is directed parallel to the z-axis. A proton enters the field with a velocity v=(4j+3k)106m/s and travels in a helical path with a radius of 5.0 cm. (a) What is the value of B? (b) What is the time required for one trip around the helix? (c) Where is the proton 5.0107s after entering the field?arrow_forwardThe velocity vector of a singly charged helium ion (mHe = 6.64 1027 kg) is given by v=4.50105m/s. The acceleration of the ion in a region of space with a uniform magnetic field is 8.50 1012 m/s2 in the positive y direction. The velocity is perpendicular to the field direction. What are the magnitude and direction of the magnetic field in this region?arrow_forward
- 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 particle moving downward at a speed of 6.0106 m/s enters a uniform magnetic field that is horizontal and directed from east to west. (a) If the particle is deflected initially to the north in a circular arc, is its charge positive or negative? (b) If B = 0.25 T and the charge-to-mass ratio (q/m) of the particle is 40107 C/kg. what is ±e radius at the path? (c) What is the speed of the particle after c has moved in the field for 1.0105s ? for 2.0s?arrow_forwardTwo long, straight wires are parallel and 25 cm apart. (a) If each wire carries a current of 50 A in the same direction, what is the magnetic force per meter exerted on each wire? (b) Does tire force pull the wires together or push them apart? (c) What happens if the currents flow in opposite directions?arrow_forward
- What is the Earths magnetic flux through a. a basketball, b. a hula hoop standing up perpendicularly on its rim at the North Pole, and c. a hula hoop lying on the ground at the North Pole?arrow_forwardA rectangular silver strip is 2.50 cm wide and 0.050 cm thick. It is in a magnetic field perpendicular to its surface (Fig. 30.41, page 957). The magnetic field is uniform, with a magnitude of 1.75 T. The strip carries a current of 6.45 A. According to Table 28.2, the number density of charge carriers in silver is 5.86 1028 m3. Find the Hall voltage for this strip.arrow_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_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning