Concept explainers
The motion of the electron inside a magnetic field of field strength of
Answer to Problem 26SP
Solution:
Electron will follow helical path of
Explanation of Solution
Given data:
The speed of the electron is
The magnitude of the magnetic field acting on the electron is
Formula used:
The radius of a charge moving along a circular path in a magnetic field is given as
Here,
The period of each revolution of a charge travelling in a circular path is given as
Here,
The horizontal (x) distance travelled by the charge during a given time (also known as pitch)is given as
Here,
Explanation:
As the electron is moving at an angle with respect to the horizontal (+x) direction, its vertical and horizontal components shall be determined as follows:
The horizontal (parallel) component of velocity will be:
Here,
Similarly, the vertical (perpendicular) component of velocity will be:
Here,
The radius of the electron moving along a circular path in a magnetic field is given as
Here,
Substitute
The period of each revolution of the electron travelling in a circular path is given as
Substitute
The horizontal (x) distance travelled by the electron during the given time (also known as pitch) is given as follows:
Here,
Substitute
Conclusion:
The motion of the electron inside a magnetic fieldwill be a helix having a radius of
Want to see more full solutions like this?
Chapter 30 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
- A long, solid, cylindrical conductor of radius 3.0 cm carries a current of 50 A distributed uniformly over its cross-section. Plot the magnetic field as a function of the radial distance r from the center of the conductor.arrow_forwardIn Niels Bohr’s 1913 model of the hydrogen atom, the single electron is in a circular orbit of radius 5.29 × 10−11 m and its speed is 2.19 × 106 m/s. (a) What is the magnitude of the magnetic moment due to the electron’s motion? (b) If the electron moves in a horizontal circle, counterclockwise as seen from above, what is the direction of this magnetic moment vector?arrow_forwardA proton (charge + e, mass mp), a deuteron (charge + e, mass 2mp), and an alpha particle (charge +2e, mass 4mp) are accelerated from rest through a common potential difference V. Each of the particles enters a uniform magnetic field B, with its velocity in a direction perpendicular to B. The proton moves in a circular path of radius rp. In terms of rp, determine (a) the radius rd of the circular orbit for the deuteron and (b) the radius ra for the alpha particle.arrow_forward
- A long, straight, horizontal wire carries a left-to-right current of 20 A. If the wire is placed in a uniform magnetic field of magnitude 4.0105 T that is directed vertically downward, what is tire resultant magnitude of the magnetic field 20 cm above the wire? 20 cm below the wire?arrow_forwardA proton travels with a speed of 3.00 106 m/s at an angle of 37.0 with the direction of a magnetic field of 0.300 T in the +y direction. What are (a) the magnitude of the magnetic force on the proton and (b) its acceleration?arrow_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_forward
- One long wire lies along an x axis and carries a current of 36 A in the positive x direction. A second long wire is perpendicular to the xy plane, passes through the point (0, 6.9 m, 0), and carries a current of 69 A in the positive z direction. What is the magnitude of the resulting magnetic field at the point (0, 1.5 m, 0)?arrow_forwardA constant magnetic field of 100 µT is directed along the positive x-axis. If a 10 µC charge is moving through this field in the direction of the y-axis at a velocity of 240 × 10^6 m/s, what is the vector force experienced by the charge?arrow_forwardA proton moves perpendicular to a uniform magnetic field B at a speed of 1.00 × 10^7m/s and experiences an acceleration of 2.00 x 10^13m/s^2 in the positive x direction when its velocity is in the positive z direction. Determine the magnitude and direction of the field. The magnitude of the magnetic field is:_____ directed toward?.arrow_forward
- An electron (charge −e) orbits with speed 2×10^6 [m/s] around a central proton (charge +e, along a circular trajectory with radius 5×10^−11 [m]. If the electron lies on the xy plane, and if the electron moves in a counterclockwise fashion as seen from the top, what is the magnetic field at the location of the proton?arrow_forwardOne long wire lies along an x axis and carries a current of 30 A in the positive x direction. A second long wire is perpendicular to the xy plane, passes through the point (0, 4.0 m, 0), and carries a current of 40 A in the positive z direction.What is the magnitude of the resulting magnetic field at the point (0, 2.0 m, 0)?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher: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 LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning