Question

Let's go through the right-hand rule. Starting with the generic vector cross-product equation $\vec{A}=\vec{B}\times\vec{C}$ point your forefinger of your right hand in the direction of $B_vec$ , and point your middle finger in the direction of $C_vec$ . Your thumb will then be pointing in the direction of $A_vec$ .

Part A

Consider the specific example of a positive charge moving in the +x direction with the local magnetic field in the +y direction. In which direction is the magnetic force acting on the particle?

Express your answer using unit vectors (e.g., $i_unit$ - $j_unit$ ). (Recall that $i_unit$ is written \hat i (or alternatively i_unit can be used.))

Direction of $F_mag_vec$ =

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Part B

Now consider the example of a positive charge moving in the +x direction with the local magnetic field in the +z direction. In which direction is the magnetic force acting on the particle?

Express your answer using unit vectors.

Direction of $F_mag_vec$ =

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Part C

Now consider the example of a positive charge moving in the xy plane with velocity $\vec{v} = v\cos(\theta)\hat{i}+ v\sin(\theta)\hat{j}$ (i.e., with magnitude at angle with respect to the x axis). If the local magnetic field is in the +z direction, what is the direction of the magnetic force acting on the particle?

Express the direction of the force in terms of , as a linear combination of unit vectors, $i_unit$ , $j_unit$ , and $k_unit$ .

Direction of $F_mag_vec$ =

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Part D

First find the magnitude of the force on a positive charge in the case that the velocity $v_vec$ (of magnitude ) and the magnetic field $B_vec$ (of magnitude ) are perpendicular.

Express your answer in terms of , , , and other quantities given in the problem statement.

=

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Part E

Now consider the example of a positive charge moving in the -z direction with speed with the local magnetic field of magnitude in the +z direction. Find , the magnitude of the magnetic force acting on the particle.

Express your answer in terms of , , , and other quantities given in the problem statement.

Answer 1

F = qV x B
A) k_hat
B) -j_hat
c) sin ? (i) - cos ? (j)

d)q*v*B

e)0
f) Bqv sin ? (i)