Question

Consider the specific example of a positive charge qqq 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^i^i_unit- j^j^j_unit). (Recall that i^i^i_unit is written \hat i (or alternatively i_unit can be used.))

Answer 1

Answer: The direction of magnetic Force (B) is in the positive z direction.

Step-by-step explanation:

The magnetic force that is acting on a charge particle into a constant magnetic field is given by this equation:

F_B = q ( v × B)

The particle is moving in the positive x direction, it means that the unit vector of the velocity will be i^.

While on the other hand, the direction of the magnetic field is in the positive direction of the y axis, so the unit vector will be j^ .

As we see, the magnetic force is given by the cross product between the velocity and the magnetic field, therefore the direction will be the product between i^ and j^. Using the right hand rule (right hand rule states that, to find the direction of the magnetic force on a positive moving charge, the thumb of the right hand point in the direction of v, the fingers in the direction of B, and the force (F) is directed perpendicular to the right hand palm) we will have:

i^ × j^ = k

meaning that the direction of the F(B) is in the positive z direction.

Answer 2

The direction of F(B) is in the positive z direction.

Step-by-step explanation:

The magnetic force acting on a charge particle into a constant magnetic field is given by this equation:

`\vec{F}_(B)=q(\vec{v}* \vec{B})`

The particle is moving in the positive x direction, it means that the unit vector of the velocity will
`\hat{i}`.

By the other hand, the direction of the magnetic field is in the positive direction of the y axis, so the unit vector of B will be
`\hat{j}`.

As we see, the magnetic force is given by the cross product between the velocity and the magnetic field, therefore the direction will be the result of the cross product between
`\hat{i}` and
`\hat{j}`. Using the right hand rule we will have:

`\hat{i} * \hat{j}=\hat{k}`

It means that the direction of F(B) is in the positive z direction.

I hope it helps you!