A charged particle of mass m -5.4x108 kg, moving with constant velocity in the y

Question

A charged particle of mass m -5.4x108 kg, moving with constant velocity in the y direction enters a region containing a constant magnetic field B- 2.6T aligned with the positive z-axis as shown. The particle enters the region at (x,y) - (0.81 m, 0) O ??? and leaves the region at (x,y)-0, 0.31 m a time t-543 ?s after itentered the' region. - 1) With what speed v did the particle enter the region containing the magnetic field? 2343 m/s Submit You currently have 5 submissions for this question. Only 10 submission are allowed. You can make 5 more submissions for this question. Your submissions: 2343 Computed value: 2343Submitted: Monday, July 16 at 10:06 PM Feedback: Your answer has been judged correct; the exact answer is: 2343.17486187845. 2) What is Fa, the x component of the force on the particle at a time ty 181 us after it entered the region containing the magnetic field. -0.031696 You currently have 4 submissions for this question. Only 10 submission are allowed N Submit You can make 6 more submisions for this question Your submissions: -0.031696 |X 0.031696Submitted: Monday, July 16 at 10:11 PM Feedback: It appears you have made a power of ten error.

Explanation / Answer

In 543 micro sec, particle rotates by 90 deg. While moving in magnetic field, speed of particle remains constant.
So in 181 micro sec, it rotates by 181*90/543 = 30 deg.

Force acting on particle is constant in magnitude and always acting toward center that is origin. At 181 micros sec. this force makes angle of 30 deg with x- axis.
magnitude of force = mv2/r = 5.4x10-8 *23432 / 0.81 = 0.366 N
x- xomponent of force Fx = - F cos 30 = -0.317 N
y-component Fy - F sin 30 = - 0.183 N

magnitude of Force F is also = q V B
0.366 = q*2343*2.6
q = 6x10-5 C
Direction of VxB , as particle enters magnetic field is along +ve x-axis, but particle has center of circle in opposite direction. Hence charge is -ve.
Hence q = -6x10-5 C

5) Radius of particle, R = mv/qB
With double velocity, B should become double so that radius or trajectory of particle remain same.
hence B should increase by factor of 2

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