Charged particles with electric and magnetic fields!!!?

Question

A charged particle moves through a region of space containing both electric and magnetic fields. The velocity of the particle is v = (7.8 multiplied by 103 m/s) x + (2.7 multiplied by 103 m/s) y and the magnetic field is B = (0.55 T) z. Find the electric field vector E necessary to yield zero net force on the particle. (Note: You may wish to use cross products in this problem. They are discussed in Appendix A.)

Answer 1

net force =0 = qE + q[v cross B]

E = - [v cross B]

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here x, y z and unit vectors (direction) indicating rerspective axes.

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A cross B = - B cross A

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E = B cross v

let E = Ex (x) + Ey (y) + Ez (z)

E = {(0.55 z) cross [(7.8*10^3) x + (2.7^10^3) y]}

E = 550 {(z) cross [7.8 x + 2.7 y]}

E = 550 {7.8 (z cross x) + 2.7 (z cross y)}

E = 550 {7.8 (y) + 2.7 (- y cross z)}

Ex (x) + Ey (y) + Ez (z) = 550 {7.8 (y) - 2.7 (x)}

comparing the coefficients of x, y, z unit vectors on both sides

Ex = -550*2.7 = - 1485 N/C

Ey = +550*7.8 = 4290 N/C

Ez =0

================== E vector

[- 1485 x + 4290 y + o z]