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9) Lorentz Force and the Cyclotron Frequency: (15 pts) A point charge q has an...
Consider the motion of particle mass m and charge q in an electromagnetic field with electric...
Consider the motion of particle mass m and charge q in an electromagnetic field with electric field vector is E and the magnetic field vector is B. The force acting on the particle is given by the Lorentz equation F = qE + qv x B (assuming non-relativistic case, v<) ( a) If there is no electric field and the particle enters the magnetic field in a direction perpendicular to the lines of magnetic flux, show that the trajectory is...
10) Mass Spectrometer: (14 pts) A charged nucleus of mass m and charge q is accelerated...
10) Mass Spectrometer: (14 pts) A charged nucleus of mass m
and charge q is accelerated through a constant potential V and
enters a region of constant magnetic field B. The nucleus then
undergoes circular motion before hitting a detector.
10) Mass Spectrometer: (14 pts) A charged nucleus of mass m and charge q is accelerated through a constant potential V and enters a region of constant magnetic field B. The nucleus then undergoes circular motion before hitting a detector....
Compute the following Derivations: 1)Derive the cyclotron frequency of a point charge moving perpendicular to a...
Compute the following Derivations: 1)Derive the cyclotron frequency of a point charge moving perpendicular to a constant magnetic field 2)Derive an expression for the charge on the capacitor as a function of time when a capacitor is being charged in an RC circuit 3)Derive an expression for the current as a function of time when a capacitor is being discharged through a resistor
(1) Cyclotron radiation Free electrons and protons will gyrate, or circle, around magnetic field lines at a frequency fgy equal to JEyrO2T m where B is the magnetic field. q is the charge of the p...
(1) Cyclotron radiation Free electrons and protons will gyrate, or circle, around magnetic field lines at a frequency fgy equal to JEyrO2T m where B is the magnetic field. q is the charge of the particle, and m is the mass of the particle. Jgyro is call the gyro frequency, and is also called the cyclotron frequency. As we discussed in class, charges which change their velocity will create electromagnetic waves If they change their velocity in a repeating pattern...
An electron (charge≈ 1.602 × 10−19 C; mass≈ 9.109 × 10−31 kg) moving at speed 200...
An electron (charge≈ 1.602 × 10−19 C; mass≈ 9.109 × 10−31 kg) moving at speed 200 m/s finds itself in a region of constant magnetic field. The magnetic field points perpendicular to the electron velocity and has strength 10−3 Tesla. (a) Find the magnitude of the magnetic force experienced by the electron. (b) The magnetic force causes cyclotron motion, so that the electron moves around a circular trajectory. Find the radius of the circular trajectory. (c) How long does it...
Page 2 Ex2.(15 pts) Find the direction of the Lorentz force acting on an electron moving...
Page 2 Ex2.(15 pts) Find the direction of the Lorentz force acting on an electron moving with a velocity v through an external B field oriented as indicated below. ero tho intorface is a power sunnly (an
5. An electron carrying charge -9 (where q=1.602e-19 C) is moving along the x axis in...
5. An electron carrying charge -9 (where q=1.602e-19 C) is moving along the x axis in the +x direction with a velocity ū(x, y, z) = 5 x 107 cm/s. a. We want to make the electron to curve to the right and eventually go in a circle clockwise in the xy plane by applying a magnetic field. To achieve that, the magnetic field should exert a force on the electron that is perpendicular to its direction of motion. Which...
True or False, no explanation needed. ( ) A charge with a velocity perpendicular to a...
True or False, no explanation needed. ( ) A charge with a velocity perpendicular to a uniform B field will move in a circular path in a plane perpendicular to the B field. ( ) A charge with a velocity perpendicular to a uniform B field will experience a magnetic force of F=qvB ( ) For a mass m to maintain a circular motion on an orbit of radius r, the needed centripetal force is mv/r. ( ) For a...
A positive charge q moves along the positive x-axis in a region of space where a...
A positive charge q moves along the positive x-axis in a region of space where a magnetic field points along the negative z-axis and an electric field points 19° below the negative x-axis (in the xy-plane) a. Draw a free body diagram indicating all forces acting on the particle. (Neglect gravity) b. What is the magnitude of the Lorentz force on the particle? c. What is the direction of the Lorentz force? Give your answer in degrees and indicate which...
A positive charge q moves along the positive x-axis in a region of space where a...
A positive charge q moves along the positive x-axis in a region of space where a magnetic field points along the negative :- axis and an electric field points 19° below the negative x-axis (in the xy-plane) a. Draw a free body diagram indicating all forces acting on the particle. (Neglect gravity) b. What is the magnitude of the Lorentz force on the particle? c. What is the direction of the Lorentz force? Give your answer in degrees and indicate...
10) Mass Spectrometer: (14 pts) A charged nucleus of mass m
and charge q is accelerated through a constant potential V and
enters a region of constant magnetic field B. The nucleus then
undergoes circular motion before hitting a detector.
10) Mass Spectrometer: (14 pts) A charged nucleus of mass m and charge q is accelerated through a constant potential V and enters a region of constant magnetic field B. The nucleus then undergoes circular motion before hitting a detector....
(1) Cyclotron radiation Free electrons and protons will gyrate, or circle, around magnetic field lines at a frequency fgy equal to JEyrO2T m where B is the magnetic field. q is the charge of the particle, and m is the mass of the particle. Jgyro is call the gyro frequency, and is also called the cyclotron frequency. As we discussed in class, charges which change their velocity will create electromagnetic waves If they change their velocity in a repeating pattern...
Page 2 Ex2.(15 pts) Find the direction of the Lorentz force acting on an electron moving with a velocity v through an external B field oriented as indicated below. ero tho intorface is a power sunnly (an
5. An electron carrying charge -9 (where q=1.602e-19 C) is moving along the x axis in the +x direction with a velocity ū(x, y, z) = 5 x 107 cm/s. a. We want to make the electron to curve to the right and eventually go in a circle clockwise in the xy plane by applying a magnetic field. To achieve that, the magnetic field should exert a force on the electron that is perpendicular to its direction of motion. Which...
A positive charge q moves along the positive x-axis in a region of space where a magnetic field points along the negative z-axis and an electric field points 19° below the negative x-axis (in the xy-plane) a. Draw a free body diagram indicating all forces acting on the particle. (Neglect gravity) b. What is the magnitude of the Lorentz force on the particle? c. What is the direction of the Lorentz force? Give your answer in degrees and indicate which...
A positive charge q moves along the positive x-axis in a region of space where a magnetic field points along the negative :- axis and an electric field points 19° below the negative x-axis (in the xy-plane) a. Draw a free body diagram indicating all forces acting on the particle. (Neglect gravity) b. What is the magnitude of the Lorentz force on the particle? c. What is the direction of the Lorentz force? Give your answer in degrees and indicate...
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