A particle of mass m, charge q and position x moves in a constant, uniform magnetic field B which points in a horizontal direction. The particle is also under the influence of gravity, g , acting vertically downwards. Write down the equation of motion and show that it is invariant under translations x -> x + x0. Obtain x = \alpha x \times n + gt + a where \alpha = qB/m, n is a unit vector in the direction of B and a is a constant vector. Show that, with a suitable choice of origin, a can be written in the form a = an. By choosing suitable axes, show that the particle undergoes a helical motion with a constant horizontal drift. Suppose that you now wish to eliminate the drift by imposing a uniform electric field E. Determine the direction and magnitude of E. Training

A particle of mass m, charge q and position x moves in a constant, uniform magnetic field B which points in a horizontal direction. The particle is also under the influence of gravity, g , acting vertically downwards. Write down the equation of motion and show that it is invariant under translations x -> x + x0. Obtain x = \alpha x \times n + gt + a where \alpha = qB/m, n is a unit vector in the direction of B and a is a constant vector. Show that, with a suitable choice of origin, a can be written in the form a = an. By choosing suitable axes, show that the particle undergoes a helical motion with a constant horizontal drift. Suppose that you now wish to eliminate the drift by imposing a uniform electric field E. Determine the direction and magnitude of E. Training

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Consider an equilateral triangle, with side length 0.477 m. At two of the vertices of this triangle, there are long straight wires carrying a current of 3.43 A out of the page. Find the magnitude of the magnetic field, in T, at the third vertex.
Write down an expression for the net force along the (tangentially to) arc of motion on a simple pendulum made of a metal rod of the length l and the mass m carrying the current I . The rod is suspended by the middle on a weightless wire of the length L in the magnetic field B and the gravitational field g perpendicular to the rod (see picture below).
A conducting rod is free to move along 2 parallel conducting rails. On one end a resistor, R, connects the two rails which forms a circuit. The rails are oriented along the y axis of a coordinate system. There is a constant magnetic B aligned with the z axis making it perpendicular to the plane of the rails and rod. If the rod is given an initial velocity of vo, and hence a kinetic energy of m*vo2 /2, mathematically demonstrate that as the rod rounds to a stop in an infinite time the power lost in the resistor as heat is equal to the initial kinetic energy.
A conducting rod of mass m = 50 g can freely slide down along the two vertical rail tracks as show below. The tracks are parallel to each other, separated by the distance l = 35 cm, and connected with a capacitance C= 151 mF (the entire system form a circuit). Find the acceleration of the rode if the there is an external uniform magnetic field B = 1.6 T perpendicular to the tracks. Take g = 9.81 m/s. O B m The acceleration, a = Units Select an answer
Please help me
Positively charged ions, with unknown charge magnitude, initially at rest, are acceleratedthrough an electric potential difference of magnitude 448 V into a region where there is auniform magnetic field of magnitude 5.00 ✕ 10−3 T. The ions travel perpendicular to themagnetic field and in a path of radius 8.00 cm. Determine the ratio of the charge to the mass(q/m) of the ions (in C/kg). Clear written steps of approach required.Hints: You will need to find the velocity as it enters the magnetic field. Relate force to mass
A proton is shown moving at a constant velocity near a very long wire with a steady current I. At that instant, the proton has a velocity vo i and it is lying on the xy-plane at a distance a from the wire. (i, j, k) are the unit vectors in thedirection of (+x, +y, +z), respectively +y a I) +Z +X What is the magnetic field at the position of the proton? MOI 2πα -i мот 2πα нот Σπαλ нов -k 2πα ·k
A particle of mass m = 1.5 x 10-16 kg and charge q = 2.3 × 10-16 C first accelarates under a potential difference of V = 103 V then enters a uniform magnetic field of a magnetic field vector directed vertically to the path of the particle. It is observed that the particle comes out of the uniform B field region in the reverse direction with a trajectory paralell to the original path which is shifted by Ax as seen in the figure below. It is measured that the particle spends 2.5 × 10-3 s in the magnetic field region. (a) What is the shift Ax for the trajectory? (b) What is the magnitude and direction of the magnetic field? (c) Now a second charged particle of unkown mass and charge Q = 8.5 x 10-15 C enters the same magnetic field region under the same accelerating potential. It is then observed that the radius of the trajectory of the particle in the magnetic field region is 3 x 10-² m. What is the mass of the particle? uniformm B field regian (d) Finally, a third particle of the same…
1) Except for a very long current carrying wire, the magnetic flux density B surrounds the wire and is inversely proportional to the distance from the wire axis. Let this long wire coincide with the z-axis of the cylindrical coordinate system. According to the problem: B = @ *. Find the divergence of this vector field (r, 9, z) in cylindrical coordinates.
A negatif charge q= 2.20 x10-19 C moves with a velocity v=(i-3j+2k) m/s through a region where both a uniform magnetic field and a uniform electric field exist. (a) Calculate the total force vector on the moving charge (in unit-vector notation), taking magnetic field vector B = (2i - 4j + 2k) I and electric field vectör E = (i + 2j - 3k) V/m. (b) Calculate the magnitude of the total force.
Two thin circular wires, each with radius a, carry equal currents I but in opposite directions. They are placed so that their centers are at z = ±a/2 and the plane of each loop is parallel to the xy- plane. Find the magnetic field at a point (0, 0, 2) on the symmetry axis. What is the magnetic dipole moment of the system? Expand B(z) for z ≫ a keeping the lowest order term in a/z.
In cylindrical coordinates (p, o, z), the vector potential A 0 = Hol O = - OB= 2mp OB=W = 2″ Pat a point p distance from the z axis. Find the corresponding magnetic field B