Effect of a Magnetic Field on a charge

[noops15]

1. Okay so thsi comes from Oct/Nov 05 Physics Paper 4. Question 5 b (ii) 1. The diagram shows a magnetic field into the paper and an electron moving in a straight horizontal line about to enter the field. The question asks what effect is there on the deflection of the electron if the potential difference accelerating the electron intially is reduced.



2. How should I approach this?



3. I assumed that according to F=Bqv, a decrease in v would cause a decrease in F and thus cause a smaller deflection on the electron. But the answer says otherwise because they used the Centripedal Force equation in solving this one. Why is F=Bqv not accepted?

 

[Idoubt]

Can you post what they say the answer is? and how they arrived at it?

 

[noops15]

It says that a decrease in potential difference would decrease v and thus cause a larger deflection. Thats all it says. I'm assuming they used F=mv^2/r to come to that conclusion.

 

[Idoubt]

well, if a moving electron enters a magnetic field, it will experience a force perpendicular to it's velocity and hence move in a circle ( F = qv*b) , you agree?

 

[noops15]

agreed

 

[Idoubt]

whenever you have a circular motion, there needs to be a constant radial force ( the centripetal force ) which will point towards the centre of the circle. And if the circle has a radius r, then this force HAS to be equal to

F = mv² /r

so what that is saying is that, our force here qvB, has to be equal to mv²/r

if it weren't, the electron would not go around in a circle ( of radius r) .

So, we have qvb=mv²/r

or r = mv/qb

Now what happens to r when we reduce v?

 

[noops15]

ohhhhhh! so simply because its a circular motion therefore we equate the two equations...i see...so yeah then the radius decreases implying the deflection is larger! thanks a bunch!

 

[Idoubt]

You can use F=qv*B anytime there is a moving charge in a magnetic field ( its only qvb if the velocity and magnetic field are perpendicular )

in your problem the force the particle experiences is F=qvb, but because this force is always constant perpendicular to the velocity, it becomes circular motion, and for circular motion

F_radial = mv²/r , If your question was, the moon going around the Earth in a circular path , then

GM_earthm_moon/r²= mv²/r

or if it was a ball on a string

Tension = mv²/r


basically the condition for any object to move in a circle is to experience a constant radial force of magnitude mv²/r

 

[noops15]

amazing man, everything I needed to know:) thanks dude!

 

[Idoubt]