Sheet 04 Charged Particle Moving in Uniform Electric Field.
A magnetic field of \(5\times10^{-4}T\) just balances a perpendicular electric field of \(15kVm^{-1}\) in their effect om an electron beam passing through the two fields in a direction perpendicular to both of them. What is the speed of electron?
Ans: \(v=\left(3\times10^{7}\right)\frac{m}{s}\).
An electron travels in a circular path of radius \(20cm\) in a magnetic field of \(2\times10^{-3}T\) . Calculate: the speed of the electron . What is the potential difference through which the electron must be accelerated to acquire this speed?
Ans: \(V=\left(1.42\times10^{4}\right)Volt\).
Calculate: the ratio of the radii of the paths when an electron and a proton enters at right angles to a uniform magnetic field with same (a)Velocity. (b) Momentum. (c) Kinetic Energy. Given: \(\frac{m_{p}}{m_{e}}=1840\)
Ans:(a) \(\frac{r_{p}}{r_{e}}=1840\) (b) \(\frac{r_{p}}{r_{e}}=1\) and (c) \(\frac{r_{p}}{r_{e}}=\sqrt{1840}=42.89\).
Copper has \(80\times10^{28}\) electrons per unit cubic metre. A copper wire of length \(1m\) and cross-sectional area \(8.0\times10^{-6}m^{2}\) carrying a current and lying at right angle to a magnetic field of strength \(5\times10^{-3}T\) experiences a force of \(8.0\times10^{-2}N\) . Calculate: drift velocity of free electrons in wire.
A beam of alpha particles and of protons of same velocity \(V\) , enters a uniform magnetic field at right angle to the field lines. The particle describes the circular paths. What is the ratio of radii of the two circles?
Ans: \(\frac{r_{\alpha}}{r_{p}}=2\).
An electron moving horizontally with a speed of \(4\times10^{4}ms^{-1}\) enters a region of uniform magnetic field of \(10^{-5}T\) acting vertically downwards as shown in below figure. Draw the trajectory and find out the time it takes to come out of the region of magnetic field?
Ans: \(t=\left(1.8\times10^{-4}\right)s\).
An electron after being accelerated through a potential difference of \(10^{4}V\) enters a region of uniform magnetic field of \(0.04T\) perpendicular to the direction of motion. Calculate: radius of curvature of its trajectory.
Ans: \(r=\left(9.64\times10^{-3}\right)m\).
A beam of protons enters an uniform magnetic field of \(0.3T\) with a velocity \(4\times10^{5}ms^{-1}\) at an amgle \(60^{o}\) to the field. Find: the radius of the helical path taken by the beam. Also, find the pitch of the helix i.e. distance travelled by a proton parallel to the magnetic field during one period of ratio. Given: \(m_{p}=1.67\times10^{-27}Kg\) .
Ans: \(r=\left(12\times10^{-3}\right)m=1.2cm\) and \(p=\left(43.5\times10^{-3}\right)m=4.35cm\)
In a chamber of uniform electric field of \(8.0G\left(1G=10^{-4}T\right)\) is maintained. An electron with a speed of \(4.0\times10^{6}ms^{-1}\) enters the chamber in a direction normal to the field. (i) Describe the path of the electron. (ii) What is the frequency of revolution of electron? (iii) What happens to the path of the electron if it progressively loses its energy due to the collision with the atoms or molecules of the environment?
Ans:(i) \(r=\left(2.8\times10^{-2}\right)m=2.8cm\) (ii) \(\nu=\left(0.22\times10^{8}\right)Hz=22MHz\) and (iii) \(\).
A solenoid of length \(1.5cm\) and has a total of \(1500\) turns wound on it. If carries a current of \(3A\) . Calculate: the magnitude of the magnetic field inside the solenoid, what would be the force experienced by this electron?
