An electron moving along the positive x axis perpendicular to a magnetic field experiences a magnetic direction in the negative y direction. What is the direction of the magnetic field?
F = q V x B, where V and B are vectors and x is the vector cross product. Note that the V comes before the B in the cross product; if it were B x V, the direction would be opposite. In this case, qV is in the -x direction because of the minus sign of q. The force is the -y axis. One assumes that the direction of z is up "out of the page" when looking at the x-y plane.
To have a force F along the -y axis, the B field must be along the -z axis (down). That is because one uses the right hand rule when taking the cross product of qV (along -x) and B (along -z).
Oh, magnetic fields can be quite sneaky, just like a mischievous clown! If an electron moving along the positive x axis is feeling a magnetic force in the negative y direction, then the magnetic field must be pointing into the positive z direction. It's like the field is saying, "Hey, electron, don't go that way, go up!" Just like a circus act, sometimes physics can be a bit topsy-turvy!
To determine the direction of the magnetic field, we can use the right-hand rule for a moving charged particle in a magnetic field.
1. Place your right hand with the thumb pointing in the direction of the electron's velocity (positive x-axis).
2. Extend your index finger perpendicular to the velocity (parallel to the magnetic field).
3. The palm of your hand will face in the direction of the force experienced by the electron (negative y-axis).
According to the rule, since the force is directed downward (negative y-axis), the magnetic field must be directed into the page or screen, opposite to the direction of the electron's motion along the positive x-axis.
To determine the direction of the magnetic field, we can use the Right-Hand Rule for a moving charge in a magnetic field. According to the right-hand rule, if you point your right thumb in the direction of the current or the moving charge and curl your fingers, the direction of the magnetic field lines will follow the direction in which your fingers curl.
In this scenario, we have an electron moving along the positive x-axis and experiencing a magnetic force in the negative y-direction.
To apply the right-hand rule, imagine your right thumb pointing along the positive x-axis. Now, curl your fingers to align with the negative y-direction, which represents the direction of the force on the electron.
To determine the direction of the magnetic field, your fingers would have to curl in the opposite direction. Therefore, the magnetic field lines would point out of the plane of the page, perpendicular to the x and y-axis, in the positive z-direction.