Question letters a, b, and c Thank You A charge moving at right angles to a uniform B (Into the page)field moves in a circle at constant speedbecause F and v are always perpendicular toyeach other.aF(A)(В)Figure 1:1. A proton moves perpendicular to a uniform magnetic field B at a speed of 1.00 x 107 m/s and experiences an acceleration of 2.00 x 1013 m/s2in the negative x-direction when its velocity is in the positive y-direction[see figure 1(A)).(a) The radius r, The cyclotron angular velocity we, the magnitude and direction of the field can be found as follows[mp1.66x10-27kg, q =1.60 x 10-19C]. Since ac == 5m, and we = "t = 2 x 106 Rad/s = B and from the second law: qvi Bsin90° = mpac - B =mpacqut= 0.021T and the direction of the field is into the page as indicated in the figure 1A (True, False).The acceleration, the velocity and the position can be written as[see figure 1(B)][ = we → ¢ = wct + ¢o = wet and ro is a constantvector]är = -ac(cos oi + sin o3) = ac(-p)(ь)a = at(- sin oi + cos oi = a,ô = dut ô = 0 - a = är + ãt +ã, = ac(-ê) (True, False)az =d k = 0(c) The work done by the magnetic field is zero . This implies that the magnetic field can not change the speed of the particle(True, False)

Given that:Speed of proton: v→=(1.00×107 m/s ) j^Acceleration, a→=-(2.00×1013 m/s2) i^ a) Centripital acceleration:ac=vt2rr=vt2ac=(1.00×107)22.00×1013=5 mAngular velocity:ω=vtr=1.00×1075=2×106 rad/sFrom Lorentz force:mω2r=qvtBmω2r=qωrBω=qBmAlso from 2nd law:q(vt→×B→)=mpacqvtBsin90°=mpacB=mpacqvtB=(1.66×10-27×2×1013)(1.6×10-19×1×107)=0.021 T So the statments of part a is true.b) Here centripital acceleration:ac→=ac(-r^)ac→=-ac(cosϕi^+sinϕj^)=ac(-ρ^)Here, ρ^= Unit vector along the direction of ρHere, the tangential velocity is constant, So at=0Also, the motion is confined in the 2D plane XY plane, therefore the z componentof accleration is zero. az=0nce the statements given in part b is true.c)From work energy theorem, the net work done is equal to change in kinetic energy. So since net work done is zero by the magnetic field, the speed remains constantThe magnetic field does not change the speed of the particle, it just supplies the required centripital force. (True)