Moving Charges and Magnetism Notes

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MOvInG ChArGeS MaGnEtIsM Classmate BEST NOTES All Previous Year Q s ApNIKAkSHA o ignoring s s MOVING CHARGES AND MAGNETISM tf Oersted s experiments Hans Christian Oersted noticed that a current carrying wire caused a noticeable deflection in a nearby magnetic compass needle On conducting a few experiments he found that The compass needle aligns tangentially to an imaginary circle at the center of which is the current carrying wire and whose plane is perpendicular to the wire The deflection increases on bring the wire closer to the needle or increasing the current Iron filings sprinkled around the wire arrange themselves in concentric circles with the wire as the center Reversing the direction of current reverses the direction of orientation of the compass needle Conclusion Moving charges or currents produce a magnetic field in the surrounding space Note Important convention Current emerging out of the plane is depicted by a dot going into the plane is depicted by a cross Magnetic field B Like static charges produce electrostatic field moving charges produce both electrostatic and magnetic field It is a vector quantity SI Unit Tesla T or Webber meter 2 Wb m 2 cgs unit Gauss G 1G 10 4 T Principle of superposition of magnetic field Total magnetic field at point due to multiple sources is the vector sum of all magnetic field of each individual source Magnetic force PYQ 2020 2019 2018 2017 2016 2014 2013 2011 1 Magnetic Force on a moving charged particle The magnetic force Fb on charge q moving with velocity v in a magnetic field B is given as It depends on q v and B Force on a negative charge is opposite to that on a positive charge The magnetic force q v B includes a vector product of velocity and magnetic field So force will always be perpendicular to v and B Direction of force is given by cross product rule or Flemings left hand rule Since Fb is perpendicular to v the work done by magnetic force is always zero i e in a magnetic field speed of particle remains constant only the direction of velocity can change Magnetic force becomes zero when v 0 i e only moving charges can experience magnetic force Magnetic force depends on the frame of reference Magnetic force becomes zero when v is parallel to B i e when particle is moving along or opposite to the field it experiences no magnetic force Case 1 v is perpendicular to B If a charged particle moving with velocity v enters a Magnetic field B perpendicularly the force acts such That the particle moves in a circular path see fig with The same speed v Let radius of circle be r The magnetic force that the Particle experiences provides the centripetal force Required to move in the circle Therefore we can write T q Be B FI E I q B Where p is momentum KE is kinetic energy and V is potential difference i7 e 2m 2e 4m e m 1840 Charge e Mass m Proton Electron Alpha particle Deuteron Time period of the particle is independent of speed and radius of the particle i e if a charged particle of mass m and charge q enters a magnetic field with different velocities in each case its time period remains same Note Use the following table to quickly solve the questions asking you to compare Time period and radius of various charged particles in magnetic fields Important PYQs Ques An alpha particle is accelerated through a potential difference of 10kV and moves along the x axis It enters in a region of uniform magnetic field B 2 10 3 T acting along the Y axis Find the radius of its path mass of alpha particle 6 4 10 27 kg PYQ 2020 3M Ans Ques An alpha particle and a proton of the same kinetic energy are allowed are in turn allowed to pass through a magnetic field B acting normal to the direction of the motion of the particles Calculate the ratio of radii of the circular paths described by them PYQ 2019 1M Ans Ques a Write the expression for the magnetic force acting on a charged particle moving with velocity v in the presence of magnetic field B b A neutron an electron and an alpha particle moving with equal velocities enter a uniform magnetic field going into the plane of the paper as shown in the fig Trace their trajectories and justify your answer PYQ 2016 Ans a F q v B b The neutron will not be deflected as it is neutral in nature The electron and the alpha particle will go around circular trajectories since they enter perpendicular to the field However they will be deflected in opposite directions as they are oppositely charged however they both wont be able to complete their circular trajectories as they will exit the field P I p l D O V cosO B USino V Ques A proton and deuteron having equal momenta enter a region of uniform magnetic field at right angle to the direction of the field Depict their trajectories in the field PYQ 2013 2M Ans They will both move in circular trajectories Case 2 v is inclined to B at an angle If a charge q enters a magnetic field at an angle other than 90 It will not move in a perfect circular path Instead it will move in A helical path This can be explained by resolving the velocity into Components The component parallel to field will experience no Force and hence continue moving in the same straight path The Component perpendicular to the field will experience a force due To which the charge will move in a circle The net result of these two Will result in a helical trajectory of the charge To calculate the radius we will take the perpendicular component only hence Pitch it is the forward distance moved in one complete revolution Only the parallel component will contribute to the pitch hence Important PYQ Ques Two protons of equal kinetic energies enter a region of uniform magnetic field The first proton enters normal to the field direction while the other enters at angle of 30 to the field direction Name the trajectories followed by them PYQ 2018 1M Ans The first will go around in a circular trajectory and the other will go in a helical path Motion in combined electromagnetic field Lorentz force PYQ 2014 2011 Consider a charge q moving with velocity v in a region with both electric E and magnetic field B the charge will experience both electrostatic and magnetic force This was first given by H A Lorentz therefore it is called Lorentz force f E Ff Pitch S s E F E i 7 If net F 0 Important PYQs Ques Write the expression in a vector form for the Lorentz magnetic force F due to a charge moving with velocity v in a magnetic field B What is the direction of force PYQ 2014 Ans F q v B The magnetic force acts in a direction

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