B field Concept Tests B 1 A negative particle and a positive particle are moving with certain velocities in a constant uniform magnetic field B as shown The direction of the B field is to the right The particle is moving directly left the particle is moving directly up B The force on the positive particle due to the B field is in into page out out of page A in B out C zero D right E left The force on the negative particle due to the B field is A in B out C zero D right E left Answers The particle is moving anti parallel to the B field The angle is 180 and the force is FB qvB sin 0 The particle is moving at right angles to the field By the right hand rule the direction v cross B is into the page but the particle has a negative charge q so the force is out of the page B 2 A positive particle is released from rest in a region of space where there is constant uniform electric field E and a constant uniform magnetic field B The electric field points up and the magnetic field points out of the page in the diagram below Which path will the positive particle follow All paths shown are in plane of the page A E B C B out D it will remain stationary Answer The particle will feel a force FE qE due to the E field along the direction of the E field As it starts moving along the E field direction it will acquire a velocity and it will start to feel a force FB qvB due to the B field The direction of the force is to the right by the right hand rule B 3 A charged particle with an initial speed vo is moving in a plane perpendicular to a uniform magnetic field B into the page There is a tenuous gas throughout the region which causes viscous drag and slows the particle over time The path of the particle is A a spiral inward B a spiral outward B C something else If the time for the particle to complete the first revolution once around is 1 second the time for the first 5 revolutions is A 5 s B 5 s C 5 s Answers It will spiral in As the particle s speed v decreases its orbital radius decreases according to R mv qB The period is 5s The period T and the frequency f 1 T are independent of the radius R or the speed v The cyclotron frequency is f qB 2 m As the speed v decreases the radius R decreases in proportional It moves more slowly but around a smaller circle so the time to go around once remains constant B 4 A square loop of wire carrying current I is in a uniform magnetic field B The loop is perpendicular to B B out of the page What is the direction of the net force on the wire A out of the page B into the page B C D E None of these I The same loop is now in a non uniform field B Bz where B B y A y where A is a constant The direction of the net force is B stronger B A C B weaker D E net force is zero Answers When the B field is uniform the net force is zero The force on each side is F I L B where L is the edge length The forces on each edge each point away from the square and so they cancel In the non uniform B field the net force is upward since the upward force on the top wire is larger than the downward force on the bottom wire B 5 A particle with unknown charge but non zero q and moving left with speed v enters a regions where there is a uniform electric field down and a uniform magnetic field out of the page The particle is observed to go in a straight line The charge of the particle must be A positive B negative C impossible to determine B Suppose the particle is a proton If the speed of the proton is increased it will A still undergo no deflection B deflect out of the plane of the page v C stay in the plane of the page and deflect upward D stay in the plane of the page and deflect downward E Answers Impossible to tell the sign of the charge It is possible that the charge could be either positive or negative If the charge is positive the force from the E field is down the force from the B field is up and the forces cancel But if charge is negative both forces switch direction and the forces still cancel In either case the fact that the particles is moving with constant velocity implies that Fnet 0 Since the net force is zero the magnetic force magnitude q vB must cancel the electric force magnitude q E So we have vB E the q s cancel so only particles with speed v E B pass straight thru regardless of the sign or magnitude of the charge This device is called a velocity selector only particle with this speed go straight thru any other speed will result in a curving trajectory FE qE FB qvB v B v FB qvB E FE qE As the speed of the proton increases its trajectory stays in the plane of the page and deflects upward If the speed v is increased the upward magnetic force FB qvB is increased but the downward electric field force FE qE remains the same
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