Question

Five equal-mass particles (a–e enter a region of uniform magnetic field directed into the page. they follow the trajectories illustrated in (figure 1 . part a which particle (if any is neutral?

Answer 1

We have particle A which is curved to the left-hand side.
Particles B is slowly bent to the right side.
Particle C curves towards the right side.
Particle D is perpendicularly straight. 
The particle E bends towards the right side.
 Therefore D is showing none deflection then it is the part D which is neutral

Answer 2

Particle D is neutral

Further explanation

Magnetic fields can be generated by:

• 1. a moving charge
• 2. current element
• 3. straight electrical wire
• 4. electrical wire coiled

The charge of a moving electron experiences a magnetic force.

The magnetic force (Lorentz) acting on a charge moving in a magnetic field is:

F = B i l sin α

F = magnetic force, N

B = magnetic induction, Wb / m²

i = electric current, A

l = length of conductor, m

α = angle between current and magnetic field

The path traveled by the charge over time is proportional to velocity (v = l / t), while the current I = q/t

so the magnetic force equation becomes

F = Bqv sin a

If we look at the picture, the particle enters the magnetic field perpendicularly so that the magnetic force functions as a centripetal force

F = Bqv sin 90 = m.ac (ac = centripetal acceleration)

$\displaystyle Bqv=m\frac{v^2}{r}$

$\displaystyle r=\frac{mv}{Bq}$

From this equation shows that the radius of the path of a particle is proportional to its linear velocity

From the picture also shows that particle D is not deflected in a magnetic field, so that the path moves straight, so the magnetic force = 0, can also show neutral charged particles because there is no magnetic force acting on it

Learn more

the average velocity

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resultant velocity

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velocity position

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Keywords: Centripetal force, linear velocity,  magnetic force, Lorentz