Magnetic Fields

When placing a compass at different positions around the magnet, we saw the the compass needle pointed in different directions at each location. The arrows drawn are the direction the arrows pointed at each location.

The magnetic field of a magnetized object points from the north end of the object to the south pole. Enclosing the object in a gaussian sphere results in a zero net flux.

The magnetic force created on a moving charged particle in a magnetic field is the cross product of the qv x B, where q is the charge of the particle, v is the velocity vector, and B is the magnetic field vector. For negatively charge objects, the direction of the force is opposite to that of the right hand rule. When the object is moving in a direction parallel to the field, it experiences no magnetic force.

The magnitude of the magnetic force is the equal to the product of the charge, the magnitude of the velocity vector perpendicular to the magnetic field, and the magnitude of the magnetic field. The units of the a magnetic field is N/Am, or the Tesla (T).

Here we calculated the magnetic force vector on a proton in motion. This is allows us to see the acceleration the proton experiences in the magnetic field.

When a charge particle moves perpendicular to a uniform magnetic field, the magnetic force is always perpendicular to its velocity. Therefore, the magnitude of the velocity never changes, and it experiences a radial acceleration of v^2/R. If the particle is not moving perpendicular to the the field. then the component of the velocity parallel to the mangetic field is constant, and the object path of motion traces out a helix.

The angular frequency of the charged particle moving in the magnetic field is equal to v/R. Substituting our value for R from the previous picture allows the determine the angular frequency can be represented by qB/m. (q-charge; B-magnetic field; m-mass).

We see here that the product q*v can be represented as the product of the length of the wire the a current runs along. 

Here is a depiction of two loops of wire with a current running through it. When a magnetic field flows parallel to the plane of a loop, the net force on the loop is zero, but a net torque is exerted on the loop. When field runs perpendicular to the plane of the loop, there is zero net torque and zero net force. 

Here is a current carrying wire inside a magnetic field. The field caused the wire to jump toward us. When a current carrying loop was inserted into the field, we saw that is rotated as a result of the torques experienced by the loop.

For this assignment, we need to find the total force on this current carrying half loop. All the x components of the magnetic force cancel each other out, so the only force component that matters is the y-component of force.

The y component of force equals I*L*B*sin(theta). Breaking the half circle up into 15 segments provides a turn of 12 degrees for each segment. The the length L is equal to the radius multiplied the change in degrees. F=I*R*d(theta)*B*sin(theta).