A charged particle of mass m 78X108 kg moving with constant

A charged particle of mass m = 7.8X10^-8 kg, moving with constant velocity in the y-direction enters a region containing a constant magnetic field B = 2T aligned with the positive z-axis as shown. The particle enters the region at (x,y) = (0.76 m, 0) and leaves the region at (x,y) = 0, 0.76 m a time t = 787 ?s after it entered the region.

1)

With what speed v did the particle enter the region containing the magnetic field?

xxx    m/s

2)

What is F_x, the x-component of the force on the particle at a time t₁ = 262.3 ?s after it entered the region containing the magnetic field.

xxx N

3)

What is F_y, the y-component of the force on the particle at a time t₁ = 262.3 ?s after it entered the region containing the magnetic field.

xxxx N

4)

What is q, the charge of the particle? Be sure to include the correct sign.

xxx ?C

5)

If the velocity of the incident charged particle were doubled, how would B have to change (keeping all other parameters constant) to keep the trajectory of the particle the same?

a. Increase B by a factor of 2

b. Increase B by less than a factor of 2

c. Decrease B by less than a factor of 2

d. Decrease B by a factor of 2

e. There is no change that can be made to B to keep the trajectory the same.

Motion in a Magnetic Field 1 1 2 3 4 5 A charged particle of mass m = 7.8x10-8 kg, moving with constant velocity in the y-direction enters a region containing a constant magnetic field B 2T aligned with the positive z-axis as shown. The particle enters the region at (x,y) (0.76 m, 0) and leaves the region at (x,y)-0, 0.76 m a time t-787 s after it entered the region 1) With what speed v did the particle enter the region containing the magnetic field? /s Submit You currently have 0 submissions for this question. Only 5 submission are allowed. You can make 5 more submissions for this question. 2) what is Fx, the x-component of the force on the particle at a time t = 262.3 s after it entered the region containing the magnetic field N Submit You currently have 0 submissions for this question. Only 5 submission are allowed You can make 5 more submissions for this question. 3) what is Fy, the y-component of the force on the particle at a time t1-262.3 s after it entered the region containing the magnetic field N Submit You currently have 0 submissions for this question. Only 5 submission are allowed. You can make 5 more submissions for this question. 4) What is q, the charge of the particle? Be sure to include the correct sign C Submit You currently have 0 submissions for this question. Only 5 submission are allowed. You can make 5 more submissions for this question. 5) If the velocity of the incident charged particle were doubled, how would B have to change (keeping all other parameters constant) to keep the trajectory of the particle the same? O Increase B by a factor of 2 0 Increase B by less than a factor of 2 O Decrease B by less than a factor of 2 O Decrease B by a factor of 2 O There is no change that can be made to B to keep the trajectory the same Submit You currently have 0 submissions for this question. Only 5 submission are allowed. You can make 5 more submissions for this question.

Solution

1. Velocity = {pi*d}/ 2t = pi*(0.76)/2*787*10^-6 = 1516.9 m/s

2. Angle = vt\'/d =1516.9*262.3*10^-6/0.76 = 0.52353 rad= 29.996 = 30^o

thus x component of the force:

    F = [mv^2/r] * cos30 = {(7.8 *10^-8) *(1516.9)^2*cos 30}/0.76 = 0.2045 N
3.

The y-compoentn of the force:

F = [mv^2/r] * sin30 = {(7.8 *10^-8) *(1516.9)^2*sin 30}/0.76 = 0.118 N

4.

the charge is calculated as follows:

    q = mv/Bd = [(7.8 *10^-8) *(1516.9)] /2*0.76 = 77.84x10^-6 C = 77.84 uC

5.

fireld B is proportional to v, so the field is increased by a factor of 2.