Calculating Angle for Magnetic Force of 2.2F

[buckeyes]

When a charged particle moves at an angle of 19° with respect to a magnetic field, it experiences a magnetic force of magnitude F. At what angle (less than 90°) with respect to this field will this particle, moving at the same speed, experience a magnetic force of magnitude 2.2F?

 

[buckeyes]

i have no idea where to begin

 

[wysard]

Not enough information given. Is the particle stationary at start, or in motion? If in motion what is its initial position and vector with respect to the source of the field? It is important because you posit that the solution requires that the particle be moving at the same speed, but do not indicate what that speed is. It looks like (on first blush) that you are looking for a deflection force solution, but without knowing what the source strength is, and the relative velocities are a definitive solution is not easy to express.

 

[buckeyes]

i don't know... this is all of the information that the homework problem provides.

 

[wysard]

OK. Let's take that the question is poorly worded, and work from there. The particle, regardless of velocity, is vectored. If it were not, say it was running directly away from the source, it would slow down, stop, and then fall toward the field. If it was running straight into the source, it would experience an increasing F gradient, but no deflection angle.

The largest deflection in a particle always occurs at right angles between the particle and the source, regardless of relative masses and velocities. (This completely disregards the effect of the forces on the final vecors of the the masses in question, but c'est la vie)

So, if the largest deflection is F at radius 1 (arbitrary, chosen for unit circle and easy lookup in standard tables for cos and sin) is 19 degrees. The question breaks down to this: At what radius from the source (less than 1) does the inverse square law yield a field strength of 2.2. Then, if the particle was at 19 degrees to point 1, what angle is it to point 2?