The force on a charged particle due to electric and magnetic fields is given by F = q E + q u x B. Suppose is along the X-axis and along the Y-axis. In what direction and with what minimum speed υ should a positively charged particle be sent so that the net force on it is zero?

According to the problem, the net electric and magnetic forces on the particle should be zero.


i.e.,


F=qE +qν ×B =0


E=-ν ×B So, the direction of × should be opposite to the direction of .


Hence, should be along the positive z-direction.


Again,




For ν to be minimum,


θ=90° and, thus,


So, the particle must be projected at a minimum speed of E/B along the z axis.


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