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Direction in electric fields

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Jimbo123:
Morning all,

I need some help with the below question.  I have calculated the magnitude of the final velocity but I haven't been taught how to find the direction. Do you use trig to find the final velocity's direction and how do you word it?

An alpha particle, with charge +3.2 × 10−19C and mass 6.6 × 10−27 kg, enters a vertical, uniform electric field
at an angle of 30° to the field. The field points upwards and has a magnitude 30Vm−1. The initial speed of the alpha particle is 150 km/s.

a Draw a diagram showing the field and the trajectory of the particle in the field.
b Calculate the velocity of the alpha particle 5.0 s after entering the field. Give the magnitude and
direction of the velocity.

Cheers

Bri MT:
Do you know the right hand rule?

(I did VCE not HSC but) my approach would be to use trig.

Wording is generally "into the page", "right" etc and indicating angles where appropriate.

Hope this helps :)

jamonwindeyer:
Hey Jimbo! You’re spot on - I imagine you found a horizontal and vertical velocity in your first answer and then used Pythagoras to get the magnitude? If so, all you need to do is some right angled trigonometry to get the angle (tanx should be what you use!)

Then as miniturtle says, you can give the reference point for the angle in a few ways. I’d do it with respect to the field (which is vertical), so say “22 degrees from the direction of the field”

zhudiac:
Hi,

Attached is part (a). I'm still working on part (b) but it seems quite complex, not quite as straight forward as it may seem due to the 3D motion it undergoes. Will post ASAP.
Please correct me if anything is wrong with my answer. Thanks!

zhudiac:
Hi,

Attached is the answer to part (b). Please correct me if my working was wrong.

For HSC, I think that the question is actually a purely qualitative question; you only need to state that it is at the same velocity as starting; as the velocity magnitude is unchanged (by definition) in uniform circular motion, and that the angle to the B-field is unchanged also as the force due to the magnetic field is only acting on the horizontal plane, not affecting the helical path of the alpha particle.

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