The relationship between charge and magnetic field is that a charged particle moving through a magnetic field will experience a force perpendicular to both the direction of its motion and the direction of the magnetic field. This force is known as the Lorentz force and is given by the equation F = qv x B, where q is the charge of the particle, v is its velocity, and B is the magnetic field.
The direction of the magnetic field will determine the direction of the force experienced by a charged particle. If the magnetic field is perpendicular to the particle's motion, the force will be perpendicular to both the field and the particle's velocity, causing the particle to move in a circular path. If the magnetic field is parallel to the particle's motion, there will be no force acting on the particle.
A uniform magnetic field has a constant magnitude and direction throughout the entire field. This means that a charged particle will experience the same force at all points within the field. A non-uniform magnetic field has varying magnitudes and/or directions at different points within the field, causing the force on a charged particle to vary as well.
The strength of the magnetic field, represented by the symbol B, directly affects the force experienced by a charged particle. The stronger the magnetic field, the greater the force on the particle will be. This can be seen in the equation F = qv x B, where B is in the denominator, meaning that as B increases, the force increases as well.
Some real-world applications of the relationship between charge and magnetic field include electric motors, particle accelerators, magnetic resonance imaging (MRI) machines, and generators. In these devices, the interaction between charged particles and magnetic fields is utilized to produce motion, generate electricity, or create images of the human body.