Electromagnetism and Magnetic Fields
Tuesday 7-15-96
The relevant section in the textbook is 18.2
Main concepts:
- an electric field E exerts a force on a charge q. A magnetic field B will also exert a force on a charge q, but only if the charge is moving (and not moving in a direction parallel to the field B). The direction of the force exerted by a magnetic field on a moving charge is perpendicular to the field, and perpendicular to the velocity (i.e., perpendicular to the direction the charge is moving).
- the equation that gives the force is F=qv X B, where X represents the cross product. This is a vector equation : F is a vector, v is a vector, and B is a vector. The only thing that is not a vector is q.
- The equation F = qv X B can be broken down into two parts, the magnitude and the direction. The magnitude is given by F = qvB sin(theta), where theta is the angle between v (the velocity) and B (the magnetic field). When v and B are at 0 degrees (or 180 degrees) to each other, the force is zero. The maximum force, F = qvB, occurs when v and B are perpendicular to each other.
- The direction of the force, which is perpendicular to both v and B, can be found using your right hand, using something known as the right-hand rule. The right-hand rule works like this. Stretch your right arm out in front of you with your thumb pointing up, your first finger pointing straight ahead, and your middle finger pointing left. There should be 90 degree angles between all three digits. Now (making sure that you maintain your thumb and first two fingers in that relative position), rotate your hand and/or arm until your thumb points in the direction of the velocity and your first finger points in the direction of B, the magnetic field (these won't always be at 90 degrees to each other, but that's fine). Your middle finger will then point in the direction of the force on the charge.
- At least, your middle finger will point in the direction of the force as long as the charge is positive. A negative charge introduces a negative sign, which flips the direction of the force. So, for a negative charge your right hand lies to you, and the force on the negative charge will be opposite to the direction indicated by your finger.
- A charged particle moving in a uniform magnetic field (i.e., a field that has the same magnitude and direction everywhere) experiences this force, directed at right angles to the way it is travelling. The force will thus tend to change the direction of the particle. In a uniform field, a charge which is initially moving in a direction perpendicular to the field will travel in a circular path, with the plane of the circle being perpendicular to the direction of the field. A charge initially moving parallel to the field would experience no force, so it would keep travelling in straight-line motion, parallel to the field. A particle which is initially moving at some angle between parallel and perpendicular to the field would follow a motion which is a superposition of circular motion and straight-line motion...it would follow a spiral path. The axis of the spiral would be parallel to the field.
Demonstrations relevant to this section: