# Vectors and Velocity Problem

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A particle of charge q is started at the origin with an initial velocity (vector)v_0 = v_0 x(^), in a region where a uniform electric field exists (vector)E = E_0 z(^), and a magnetic field intensity is given by (vector)B = B_0 x(^) + B_0 y(^). HINT: ROTATE THE HORIZONTAL PLANE SO ONE OF YOUR NEW AXES LINES UP WITH THE DIRECTION OF THE RESULTANT B FIELD. Write out and solve the equations for x, y, z as functions of time. Evaluate any/all constants in your solution.

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##### Solution Summary

In this solution we solve the given problem involving vector and velocity.

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** Please see the attached file for the complete solution **

Vectors v, E and B are plotted on the x,y and z rectangular coordinate system above.

Lorentz force experienced by the charged particle is given by:

F = q(E + v X B) [where X represents the cross product]

Substituting for v, E and B we get:

=> F = q[E0 + (v0 X (B0 + B0 )] = q[E0 + (v0 X B0(+ )]

=> F = q[E0 + v0 B0 ( X + X )] ...(1)

As = 0 and X = , equation (1) reduces to:

F = q[E0 + v0 B0 ) = q(E0 + B0) ...(2)

From equation (2) it is ...

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