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Page 1 Introductory Exercise 23.1 Q.1. Write the dimensions of E/B. Here, E is the electric field and B the magnetic field. Sol. qE = Bqv sin ? [E/B] = [v] = [LT ] Q.2. In the relation which pairs are always perpendicular to each other. Sol. From the property of cross product is always perpendicular to both Q.3. If a beam o f electrons travels in a straight line in a certain region. Can we say there is no magnet ic field? Sol. both may be present and may be possible that, Q.4. A charge q = 4µC has an instantaneous velocity in a uniform magnetic field What is the force on the charge? Sol. Here, q has to be substituted with sign. Introductory Exercise 23.2 1 Page 2 Introductory Exercise 23.1 Q.1. Write the dimensions of E/B. Here, E is the electric field and B the magnetic field. Sol. qE = Bqv sin ? [E/B] = [v] = [LT ] Q.2. In the relation which pairs are always perpendicular to each other. Sol. From the property of cross product is always perpendicular to both Q.3. If a beam o f electrons travels in a straight line in a certain region. Can we say there is no magnet ic field? Sol. both may be present and may be possible that, Q.4. A charge q = 4µC has an instantaneous velocity in a uniform magnetic field What is the force on the charge? Sol. Here, q has to be substituted with sign. Introductory Exercise 23.2 1 Q.1. Can a charged particle be accelerated by a magnetic field. Can its speed be increased? Sol Magnetic force may be nonzero. Hence acceleration due to magnetic force may be nonzero. Magnetic force is always perpendicular to velocity. Hence its power is always zero or work done by magnetic force is always zero. Hence it can be change the speed of charged particle. Q.2. An electron beam projected along positive xaxis deflects along the positive yaxis. If this deflection is caused by a magnetic field, what is the direction of the field? Sol: is along position y direction, q is negative and is along positive xdirection. Therefore should be along positive zdirection. Q.3. An electron and a proton are projected with same velocity perpendicular to a magnetic field, (a) Which particle will describe the smaller circle? (b) Which particle will have greater frequency? Sol. as other factors are same. Q.4. In a region of space a uniform magnetic field 6 is along positive xaxis. Electrons are emitted from the origin with speed v at different angles. Show that the paraxial electrons are refocused on the xaxis at a distance Here, m is the mass of electron and e the charge on it. Sol. Electrons touches the xaxis again after every pitch. Therefore the asked distance is d = p = v T 11 Page 3 Introductory Exercise 23.1 Q.1. Write the dimensions of E/B. Here, E is the electric field and B the magnetic field. Sol. qE = Bqv sin ? [E/B] = [v] = [LT ] Q.2. In the relation which pairs are always perpendicular to each other. Sol. From the property of cross product is always perpendicular to both Q.3. If a beam o f electrons travels in a straight line in a certain region. Can we say there is no magnet ic field? Sol. both may be present and may be possible that, Q.4. A charge q = 4µC has an instantaneous velocity in a uniform magnetic field What is the force on the charge? Sol. Here, q has to be substituted with sign. Introductory Exercise 23.2 1 Q.1. Can a charged particle be accelerated by a magnetic field. Can its speed be increased? Sol Magnetic force may be nonzero. Hence acceleration due to magnetic force may be nonzero. Magnetic force is always perpendicular to velocity. Hence its power is always zero or work done by magnetic force is always zero. Hence it can be change the speed of charged particle. Q.2. An electron beam projected along positive xaxis deflects along the positive yaxis. If this deflection is caused by a magnetic field, what is the direction of the field? Sol: is along position y direction, q is negative and is along positive xdirection. Therefore should be along positive zdirection. Q.3. An electron and a proton are projected with same velocity perpendicular to a magnetic field, (a) Which particle will describe the smaller circle? (b) Which particle will have greater frequency? Sol. as other factors are same. Q.4. In a region of space a uniform magnetic field 6 is along positive xaxis. Electrons are emitted from the origin with speed v at different angles. Show that the paraxial electrons are refocused on the xaxis at a distance Here, m is the mass of electron and e the charge on it. Sol. Electrons touches the xaxis again after every pitch. Therefore the asked distance is d = p = v T 11 For paraxial electrons ? ˜ 0° and q = e ? Q.5. A particle of mass m and charge q is projected into a region having a perpendicular magnetic field 6. Find the angle of deviation of the particle as it comes out of the magnetic field if the width of the region is, Sol. and ? = p if L = r Q.6. An electron is accelerated through a PD of 100 V and then enters a region where it is moving perpendicular to a magnetic field S = 0.2 T. Find the radius of the circular path. Repeat this problem for a proton. Sol. Q.7. A proton, a deutron and an aparticle have equal kinetic energies. Compare the radii of their paths when a normal magnetic field is applied. Page 4 Introductory Exercise 23.1 Q.1. Write the dimensions of E/B. Here, E is the electric field and B the magnetic field. Sol. qE = Bqv sin ? [E/B] = [v] = [LT ] Q.2. In the relation which pairs are always perpendicular to each other. Sol. From the property of cross product is always perpendicular to both Q.3. If a beam o f electrons travels in a straight line in a certain region. Can we say there is no magnet ic field? Sol. both may be present and may be possible that, Q.4. A charge q = 4µC has an instantaneous velocity in a uniform magnetic field What is the force on the charge? Sol. Here, q has to be substituted with sign. Introductory Exercise 23.2 1 Q.1. Can a charged particle be accelerated by a magnetic field. Can its speed be increased? Sol Magnetic force may be nonzero. Hence acceleration due to magnetic force may be nonzero. Magnetic force is always perpendicular to velocity. Hence its power is always zero or work done by magnetic force is always zero. Hence it can be change the speed of charged particle. Q.2. An electron beam projected along positive xaxis deflects along the positive yaxis. If this deflection is caused by a magnetic field, what is the direction of the field? Sol: is along position y direction, q is negative and is along positive xdirection. Therefore should be along positive zdirection. Q.3. An electron and a proton are projected with same velocity perpendicular to a magnetic field, (a) Which particle will describe the smaller circle? (b) Which particle will have greater frequency? Sol. as other factors are same. Q.4. In a region of space a uniform magnetic field 6 is along positive xaxis. Electrons are emitted from the origin with speed v at different angles. Show that the paraxial electrons are refocused on the xaxis at a distance Here, m is the mass of electron and e the charge on it. Sol. Electrons touches the xaxis again after every pitch. Therefore the asked distance is d = p = v T 11 For paraxial electrons ? ˜ 0° and q = e ? Q.5. A particle of mass m and charge q is projected into a region having a perpendicular magnetic field 6. Find the angle of deviation of the particle as it comes out of the magnetic field if the width of the region is, Sol. and ? = p if L = r Q.6. An electron is accelerated through a PD of 100 V and then enters a region where it is moving perpendicular to a magnetic field S = 0.2 T. Find the radius of the circular path. Repeat this problem for a proton. Sol. Q.7. A proton, a deutron and an aparticle have equal kinetic energies. Compare the radii of their paths when a normal magnetic field is applied. Sol. Page 5 Introductory Exercise 23.1 Q.1. Write the dimensions of E/B. Here, E is the electric field and B the magnetic field. Sol. qE = Bqv sin ? [E/B] = [v] = [LT ] Q.2. In the relation which pairs are always perpendicular to each other. Sol. From the property of cross product is always perpendicular to both Q.3. If a beam o f electrons travels in a straight line in a certain region. Can we say there is no magnet ic field? Sol. both may be present and may be possible that, Q.4. A charge q = 4µC has an instantaneous velocity in a uniform magnetic field What is the force on the charge? Sol. Here, q has to be substituted with sign. Introductory Exercise 23.2 1 Q.1. Can a charged particle be accelerated by a magnetic field. Can its speed be increased? Sol Magnetic force may be nonzero. Hence acceleration due to magnetic force may be nonzero. Magnetic force is always perpendicular to velocity. Hence its power is always zero or work done by magnetic force is always zero. Hence it can be change the speed of charged particle. Q.2. An electron beam projected along positive xaxis deflects along the positive yaxis. If this deflection is caused by a magnetic field, what is the direction of the field? Sol: is along position y direction, q is negative and is along positive xdirection. Therefore should be along positive zdirection. Q.3. An electron and a proton are projected with same velocity perpendicular to a magnetic field, (a) Which particle will describe the smaller circle? (b) Which particle will have greater frequency? Sol. as other factors are same. Q.4. In a region of space a uniform magnetic field 6 is along positive xaxis. Electrons are emitted from the origin with speed v at different angles. Show that the paraxial electrons are refocused on the xaxis at a distance Here, m is the mass of electron and e the charge on it. Sol. Electrons touches the xaxis again after every pitch. Therefore the asked distance is d = p = v T 11 For paraxial electrons ? ˜ 0° and q = e ? Q.5. A particle of mass m and charge q is projected into a region having a perpendicular magnetic field 6. Find the angle of deviation of the particle as it comes out of the magnetic field if the width of the region is, Sol. and ? = p if L = r Q.6. An electron is accelerated through a PD of 100 V and then enters a region where it is moving perpendicular to a magnetic field S = 0.2 T. Find the radius of the circular path. Repeat this problem for a proton. Sol. Q.7. A proton, a deutron and an aparticle have equal kinetic energies. Compare the radii of their paths when a normal magnetic field is applied. Sol. Introductory Exercise 23.3 Q 1. In a certain region uniform electric field 0 ˆ E E k ?? ? and magnetic field 0 ˆ B B k ?? ? are present. At time t = 0 a particle of mass m and charge q is given a velocity 00 ˆˆ v v j v k ?? ? . Find the minimum speed of the particle and the time when it happens so. Q 2. A particle of mass m and charge q is lying at the origin in a uniform magnetic field B directed along xaxis. At time t = 0, it is given a velocity v 0 at an angle ? with the yaxis in the xyplane. Find the coordinates of the particle after one revolution. Q 3. A wire of length l carries a current i along the xaxis. A magnetic field 0 ˆˆ B B (j k) ?? ? exists in the space. Find the magnitude of the magnetic force acting on the wire. Q 4. In the above problem will the answer change if magnetic field becomes 0 ˆ ˆ ˆ B B (i j k) ? ? ? ? Solutions 1. (along negative zdirection) Electric field will make zcomponent of velocity zero. At that time speed of the particle will be minimum and that minimum speed is the other component i. e., v 0 . This is minimum when, 2. Path is helix and after one rotation only xcoordinate will change by a distance equal to pitch. 3. 4. No it will not change, as the new component of is in the direction of Introductory Exercise 23.4 Q 1. A charge q is uniformly distributed on a nonconducting disc of radius Ft. It is rotated with an angular speed a about an axis passing through the centre of mass of the disc and perpendicular to its plane. Find the magnetic moment of the disc. [Hint: Magnetic moment = q 2m ?? ?? ?? (angular momentum)] Q 2. Find the magnetic moment of the current carrying loop OABCO shown in figure. Given that, i = 4.0 A, OA = 20 cm and AB =10 cm.Read More
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