Sheet 05 Cyclotron & Magnetic Field Due To Current Through A Very Long Circular Cylinder.
A cyclotron has an oscillating frequency of \(12MHz\) and dee radius \(50cm\). Calculate: the magnetic field requires to accelerate deuterons of mass \(3.3\times10^{-27}Kg\) and charge \(1.6\times10^{-19}C\). What is the energy of the deuterons emerging from the cyclotron?
Ans: \(K_{max}=14.7MeV\).
If, the maximum value of accelerating potential provided by a radio frequency oscillator be \(25kV\) , find out the number of revolutions made by a proton in a cyclotron to achieve \(\frac{1}{5}\) of the speed of the light. Mass of the proton= \(1.67\times10^{-27}Kg\) .
Ans: \(n=375rev\).
A cyclotron’s oscillator frequency is \(10MHz\) , What would be the operating magnetic field for accelerating protons? If, the radius of the ‘dees’ is \(60cm\) , what is the kinetic energy of the proton beam produced by the accelerator? Given: \(e=1.6\times10^{-19}C\) , \(m_{p}=1.67\times10^{-27}Kg\). Express your answer is the unit of MeV.\(\left(1MeV=1.6\times10^{-13}J\right)\) .
Ans: \(K_{max}=7.4MeV\).
A alpha particle of mass \(6.68\times10^{-27}Kg\) and charge \(3.2\times10^{-19}C\) are accelerated in a cyclotron in a magnetic field of \(1.25T\) is applied perpendicular to the dees. How rapidly should the electric field between the dees be reversed? What are the velocity and kinetic energy of an alpha particle when it moves in a circular orbit of radius \(25cm\) ?
Ans: \(v=\left(1.5\times10^{7}\right)\frac{m}{s}\) and \(K.E=\left(7.5\times10^{-13}\right)J\).
In a chamber, a uniform magnetic field of \(8.0G\) is maintained. An electron with speed of \(4.0\times10^{6}ms^{-1}\) enters the chamber in a direction normal to field. (i) Describe the path of electron. (ii) What is the frequency of revolution of the electron? (iii) What happens to the path of the electron if it progressively loses its energy due to collisions with the atoms or molecules of the environment?
Ans:(i) \(r=\left(2.84\times10^{-2}\right)m=2.84cm\) (ii) \(\nu=\left(22.4\times10^{6}\right)Hz=22.4MHz\) and (iii)Follows a spiral or helical path although frequency remains contant.
An electron is accelerated through a potential difference of \(2000V\) enters a uniform magnetic field of \(0.15T\). Find: the path of the electron if the field is at \(90^{o}\) to its initial velocity and also when it makes an angle of \(45^{o}\) with its initial velocity.
Ans: \(r_{90^{o}}=1mm\) and \(r_{45^{o}}=0.7mm\).
A horizontal wire of length of \(0.1m\) long carries a current of \(5A\) . Find: the magnitude and direction of the magnetic field, which can support the weight of the wire. Assume: wire to be of mass \(3\times10^{-3}Kgm^{-1}\) .
Ans: \(B=\left(5.88\times10^{-3}\right)T\).
A conductor of length \(20cm\) is placed (i)parallel (ii) perpendicular (iii) inclined at an angle of \(30^{o}\) to a uniform magnetic field of \(2T\) . If, the charge of \(10C\) passes through it in \(5s\), find the force experienced by the conductor.
Ans:(i) \(F_{\|}=0\) (ii) \(F_{\perp}=0.8N\) and (iii) \(F_{30^{o}}=0.4N\).
A straight horizontal conducting rod of length \(0.45m\) and mass \(60g\) is suspended by the two vertical wires as its ends. A current of \(5.0A\) is set up in the rod through wires. (a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero? (b) What will be the total tension in the wire if the direction of electric current is reversed, keeping the magnetic field same as before? (Ignore the mass of the wire), Take: \(g=9.8ms^{-2}\).
Ans:(a) \(B=0.26T\) and (b) \(T=1.176N\).
A \(90cm\) long wire of mass \(50g\) carries a current \(10A\) is placed over two parallel rails. A magnetic field of magnitude \(0.3T\) acts perpendicular to the length of wire. Under the action of magnetic force, it starts from rest. What will be the speed of the wire after travelling a distance of \(10cm\) ?
Ans: \(v=3.29\frac{m}{s}\).
A short conductor of length \(5.0cm\) is placed parallel to the long conductor of length \(2.0m\) near its centre. The conductors carry currents \(5.0A\) and \(4.0A\) respectively in the same direction. What is the total force experienced by the long conductor when they are \(4.0cm\) away?
Ans: \(F=\left(5\times10^{-6}\right)N\).
A current of \(2A\) enters a corner ‘a’ of a square frame of side \(20cm\) and leaves at opposite corner ‘c’. A magnetic field \(B=0.3T\) acts in a direction perpendicular to the plane of paper as shown in figure. Find: the magnitude and direction of the magnetic force on four sides of the frame.
Ans: \(F=0.06N\).
A straight wire of mass \(200g\) and length \(1.5m\) carries a current of \(2A\). It is suspended in mid air by a uniform horizontal magnetic field \(\vec{B}\). What is the magnitude of the magnetic field?
Ans: \(B=0.65T\).
On a smooth plane inclined at an angle \(30^{o}\) with the horizontal, a thin current carrying conductor is placed parallel to the horizontal ground. The plane is located in a uniform magnetic field of \(0.15T\) in the vertical direction. For what value of current can the rod remains stationary? The mass per unit length of rod is \(0.30kgm^{-1}\).
