Question

In: Physics

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 q 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 q 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 q moving in the xy plane with velocity \vec{v} = v\cos(\theta)\hat{i}+ v\sin(\theta)\hat{j} (i.e., with magnitude v at angle theta 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, j_unit, and k_unit.
Direction of F_mag_vec =
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Part D
First find the magnitude of the force F on a positive charge q in the case that the velocity v_vec (of magnitude v) and the magnetic field B_vec (of magnitude B) are perpendicular.
Express your answer in terms of v, q, B, and other quantities given in the problem statement.
F =
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Part E
Now consider the example of a positive charge q moving in the -z direction with speed v with the local magnetic field of magnitude B in the +z direction. Find F, the magnitude of the magnetic force acting on the particle.
Express your answer in terms of v, q, B, 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)


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