A charged particle moves through a region of space containing both electric and

Question

A charged particle moves through a region of space containing both electric and magnetic fields. The velocity of the particle is V=(5.0*10^-3 m/s) x + (2.1 *10^3 m/2) y and the magnetic field is B=(0.70T) z. Find the electric field vector 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 in the textbook.) Express your answer using two significant figures. Enter the , , and components of the electric field vector separated by commas.

Explanation / Answer

net force =0 = qE + q[v cross B] E = - [v cross B] ----------------------------------- here x, y z and unit vectors (direction) indicating rerspective axes. --------------------------- A cross B = - B cross A ---------------------------- E = B cross v let E = Ex (x) + Ey (y) + Ez (z) E = {(0.7 z) cross [(5.0*10^-3) x + (2.1^10^-3) y]} E = {(0.7 z) cross [(5*10^-3) x + (2.1^10^-3) y]} E = 700 {(z) cross [5 x + 2.1 y]} E =700 {5 (z cross x) + 2.1 (z cross y)} E = 700 {5 (y) + 2.1 (- y cross z)} Ex (x) + Ey (y) + Ez (z) = 700 {5 (y) - 2.1 (x)} comparing the coefficients of x, y, z unit vectors on both sides Ex = -700*2.1 = - 1470 N/C Ey = +700*5 = 3500 N/C Ez =0 ================== E vector [- 1470 x + 3500 y + o z]

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