Deflection of a object due to magnetic field

[joej]

an object of 3.8g moves @ 180m/s perpendicular to a magnetic field of (5x10^-5)T

the object possesses a net charge of (8.1x10^-9)C

by what distance will it be deflected from its pathe due to the magnetic field after it has traveled 1.0 km


so I'm guessing I'll have to find out the radius of the curvature here, so...

F = ma

a = v^2/r

qvB = (mv^2)/r

r = (mv)/(qB)

r = (1.69x10^12)m

and... yeah... where do I go from there... or do I have to do something different?

 

[dextercioby]

Are u sure this is the original text of the problem,with these figures??I mean the curvature radius is larger than the mean distance Earth-Sun,the deflectio will be almost zero.

Daniel.

 

[joej]

yeah I'm pretty sure... just double check it now again...

m = 3.8 g
B = 5 x 10 ^ -5 T
q = 8.1 x 10 ^ -9 C
distance traveled = 1.0 km

 

[dextercioby]

I'll let u do the calculations numerically,i'll simply provide the formulas.call the distance of 1Km by d,the curvature radius by "R" and the angle subtented by 'd' $\theta$
$$d=R\theta$$ (1)
$$deflection=R-R\cos\theta$$ (2)

Since the angle is vanishingly small,u may use that,for very,very small arguments
$$\cos\theta\sim 1-\frac{\theta^{2}}{2}$$ (3)

Daniel.

 

[joej]

okay so what I get is...

angle = 0.000000000592

so I use equation 3 and I get

cos(angle) = 0.999999999999999999824768

R - R(0.999999999999999999824768) =

1690000000000 - 1690000000000(0.999999999999999999824768) = 0.00000029614208

so... 2.96 x 10 ^ -7

does that seem about right?

 

[dextercioby]

The logics is flawless.For such a weird result (deflection of a straight line of a macroscopic object which smaller than the wavelegth of visible light (therefore it cannot be seen directly)),blame the idiot that made the proble up.Hopefully it's not someone u know...

Daniel.