Question

An electron travels through a region with non-zero electric and magnetic fields. The electric field is directed into the page (-k cap), the electron is moving to the right (+ i cap), and the net force on the electron is zero. a) Which component of the magnetic field must be zero? b) Which component of the magnetic field must be non-zero?

Answer 1

b)

the electric field is into the page and electron is a negative charge. we know that a negative charge experience electric force in opposite direction of the electric field. hence electric force is in outward direction or positive z-direction.

the net force on the electron is 0

that ,means the magnetic force on electron is equal and opposite to electric force. hence the direction of magnetic force on electron is in inward direction .

the electron is moving to right and magnetic force on it is in inward direction, hence using right hadn rule, the magnetic field comes out to be in upward or positive y-direction .

so y- component of magnetic field is non-zero

a)

the x-component of magnetic field is zero . since magnetic field parallel to motion of charge does not apply any magnetic force on it .