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(a) (i) Write down an expression for the force acting on a charge moving with velocity v in the presence of both electric E and magnetic B fields. (ii) Assume that a particle of charge Q moves in the presence of a uniform magnetic field B. Find the magnitude of the momentum of the particle if it moves in a circle of radius R in the plane perpendicular to B. Sketch the trajectory of the particle if it has an additional component of velocity v parallel to B. (iii) Show that magnetic forces do no work on a charge Q. (b) Starting from the integral form of Gauss's law, derive the differential form of the law, where p is the charge density. 1 V.E=P

(a) (i) Write down an expression for the force acting on a charge moving with velocity v in the presence of both electric E and magnetic B fields. (ii) Assume that a particle of charge Q moves in the presence of a uniform magnetic field B. Find the magnitude of the momentum of the particle if it moves in a circle of radius R in the plane perpendicular to B. Sketch the trajectory of the particle if it has an additional component of velocity v parallel to B. (iii) Show that magnetic forces do no work on a charge Q. (b) Starting from the integral form of Gauss's law, derive the differential form of the law, where p is the charge density. 1 V.E=P

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(a) (i) Write down an expression for the force acting on a charge moving with velocity v in the presence of both electric E and magnetic B fields. Assume that a particle of charge Qmoves in the presence of a uniform magnetic field B. (ii) Find the magnitude of the momentum of the particle if it moves in a circle of radius R in the plane perpendicular to B. Sketch the trajectory of the particle if it has an additional component of velocity v parallel to B. (iii) Show that magnetic forces do no work on a charge Q. (b) Starting from the integral form of Gauss's law, derive the differential form of the law, where p is the charge density. V.E = 1 ·P
Transcribed Image Text:(a) (i) Write down an expression for the force acting on a charge moving with velocity v in the presence of both electric E and magnetic B fields. Assume that a particle of charge Qmoves in the presence of a uniform magnetic field B. (ii) Find the magnitude of the momentum of the particle if it moves in a circle of radius R in the plane perpendicular to B. Sketch the trajectory of the particle if it has an additional component of velocity v parallel to B. (iii) Show that magnetic forces do no work on a charge Q. (b) Starting from the integral form of Gauss's law, derive the differential form of the law, where p is the charge density. V.E = 1 ·P
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