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Let's go through the right-hand rule. Starting with the generic vector cross-product equation point your forefinger...

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

). (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 theta

, as a linear combination of unit vectors, i_unit

, and

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.

Solutions

Expert Solution

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)

genius_generous answered 2 years ago

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Let's go through the right-hand rule. Starting with the generic vector cross-product equation point your forefinger...

Solutions

Expert Solution

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