Concept explainers
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 P30.83
(a)
The sketch of the magnetic field pattern in the x-z plane due to the two wires.
Answer to Problem 83PQ
The direction of the magnetic field pattern in x-z plane is shown in figure (a).
Explanation of Solution
The direction of the magnetic field for a current carrying wire is given by the Right Hand Palm rule.
According to the right hand palm rule, the thumb of the right hand points in the direction of the current flowing in the wire, the fingers point along the point at which the magnetic field is to be calculated then the palm faces towards the direction of the magnetic field.
Here, the direction of magnetic field due to both wires is in anticlockwise direction.
Conclusion:
Thus, the direction of the magnetic field pattern in x-z plane is shown in figure (a).
(b)
The magnitude of the magnetic field due to the two wires at the origin.
Answer to Problem 83PQ
The magnitude of the magnetic field due to the two wires at the origin in zero.
Explanation of Solution
The direction of the magnetic field due to first wire and the second wire is shown as.
Write the expression forthe magnetic field due to first wire.
Here
Write the expression for the magnetic field due to second wire.
Here
Write the expression for the net magnetic field at the origin as.
Here,
Conclusion:
Substitute
Hence, the net magnetic field at the origin will be zero.
(c)
The magnitude of the magnetic field due to two wire as a function of z along the z-axis.
Answer to Problem 83PQ
The magnetic field due to two wires as a function of z along the Z-axis is
Explanation of Solution
The direction of the magnetic field for a current carrying wire is given by the Right Hand Palm rule.
The magnetic field due to both wires will be in negative X-direction at some point z above the origin.
Write the expression for the magnetic field due to first wire as.
Here,
The net magnetic field due to the second wire is same as that of the magnetic field due to the first wire.
Write the expression for the magnetic field due to second wire as.
Here,
The distance of the point along the Z-axis from the wire is given by the Pythagoras theorem.
Write the expression for the distance
Here,
Write the expression for the angle made by the position vector with the horizontal as.
Substitute
Write the expression for the net magnetic field as.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Thus, the magnetic field due to two wires as a function of z along the Z-axis is
Want to see more full solutions like this?
Chapter 30 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- One common type of cosmic ray is a proton traveling at close to the speed of light. If the proton is traveling downward, as shown in Figure P30.14, at a speed of 1.00 107 m/s, what are the magnitude and direction of the magnetic field at point B?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_forwardA Derive an expression for the magnetic field produced at point P due to the current-carrying wire shown in Figure P30.26. The curved parts of the wire are pieces of concentric circles. Point P is at their center.arrow_forward
- Figure P30.11 shows three configurations of wires and the resultant magnetic fields due to current in the wires. What is the direction of the current that gives the resultant magnetic field shown in each case?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_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
- 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 strong magnet is placed under a horizontal conducting ring of radius r that carries current I as shown in Figure P28.27. If the magnetic field B makes an angle with the vertical at the rings location, what are (a) the magnitude and (b) the direction of the resultant magnetic force on the ring? Figure P28.27arrow_forwardAn electron in a TV CRT moves with a speed of 6.0107 m/s, in a direction perpendicular to Earth's field, which has a strength of 5.0105 T. (a) What strength electric field must be applied perpendicular to the Earth’s field to make the election moves in a straight line? (b) If this is done between plates separated by 1.00 cm, what is the voltage applied? (Note that TVs are usually surrounded by a ferromagnetic material to shield against external magnetic fields and avoid the need for such a collection,)arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning