The figure below shows the path of a proton (mass mp) as it passes through two r

Question

The figure below shows the path of a proton (mass mp) as it passes through two regions of space(labeled 1 and 2) containing uniform magnetic fields of magnitudes B1 and B2, respectively. Bothfields are oriented perpendicular to the page. The proton’s path in each region is a semi-circle ofradius R1 and R2, respectively. In answering the questions that follow, make sure you defendeach of your answers with a well-reasoned argument.

1)Does the proton move faster in one region than the other? Why or why not?

2)Is the magnetic field stronger in one region than the other? If so, which magnetic field isstronger and how can you tell?

3)What are the directions of the two magnetic fields?

4) Does the proton spend more time in region 1 or region 2?

5) If we replaced the proton with an electron (mass me=5.44×10–4mp)   while leaving the rest ofthe experiment the same (i.e., same initial velocity, same magnetic fields, same starting point,etc.), how would the path followed by the electron be different?

Explanation / Answer

Here ,

as the radius of path of a charged particle is given as

r = m*V/B*q

where v is the velocity and B is the magnetic field

1)
as the magnetic force is always pependicular to the velocity of particle ,

the velocity of particle is constant in the magnetic field.hence , the proton move with same speed in both regions

2)

for same proton having same velocity , as the radius is samaller is region 2.
as radius is inversly proporational to magnetic field.

the magnetic field is stronger in region 2

3)

as force = q*V X B

in region 1 ,

magnetic field is OUT OF THE PAGE

in region 2

magnetic field is INTO THE PAGE

4)

as the speed of proton is same , but the distance is higher in region 1 ,

the prootn spends more time in region 1

5) If we replaced the proton with an electron (mass me=5.44×10–4mp) while leaving the rest ofthe experiment the same (i.e., same initial velocity, same magnetic fields, same starting point,etc.), how would the path followed by the electron be different?

as the electron have smaller mass ,

radius of path is directly proporational to the mass ,

the radius of path will be smaller for electron ,

also the direction of force on electron will be oposite and it will rotate in the oposite direction

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