Question

For questions 1-3 use the figure below and give the direction of the magnetic force on the charged particle (black dot). Note that for 1 and 2 the B-field is into the page and for 3 it is to the right. Note also the sign of the charge on the particle is given in parentheses (+) or (-). right right right left left left up up up down down down into page into page into page out of page out of page out of page

Answer 1

The magnetic force is given by the Lorentz force law and is

F = Q(v x B)

where the direction of the cross-product is given by the right-handrule.

1) For particle (1), the right-hand rule gives a cross-productdirection to the right (point your index finger of your right handalong the velocity vector of the particle and curl your middlefinger in the direction of the magnetic field, and your thumb givesthe direction of the force.) But because the charge of theparticle is negative (i.e. Q = -q), the negative sign in front ofthe Lorentz force law for this particle (F =-q(v x B)) will give a vector inthe opposite direction (to the right), so our answer is (a)right.

2) For particle (2), the right hand rule gives a direction to theright. The charge on particle 2 is positive, so theLorentzforce law just gives us a force in the direction given by the righthand rule. So our answer is (a) right.

3) For particle (3), the right hand rule gives us a direction outof the page, but because the charge on particle 3 is negative, theLorentz force law gives us a force in the opposite direction, soour answer is e) into the page.

Note that the answers I have given are the instantaneous forces onthe particles, and will not be correct the instant after themagnetic force has changed the direction of the velocities of theseparticles. Because the magnetic fields in this problem areuniform, the particles will have a continuous force on themdirected perpendicular to their velocity vector, so they will becontinuously deflected in that direction. This type of forceis identicle to a centripital acceleration, so the particles willcontinue in uniform circular motion as long as the field remainsuniform.

Zoidberg