In many cases, the effect of an electromagnetic interaction is perpendicular to its cause. Describe two different examples that illustrate this.

In this example, let's consider a charged particle, such as an electron, moving through a magnetic field. The magnetic force acting on the charged particle is given by the Lorentz force equation: F = q(v x B) where F is the magnetic force, q is the particle's charge, v is the particle's velocity vector, and B is the magnetic field vector. The cross product (v x B) represents that the force F is perpendicular to both the velocity and the magnetic field. In this case, the cause of the electromagnetic interaction is the movement of the charged particle through the magnetic field (v x B), and its effect is the magnetic force (F) experienced by the particle. Since the force is perpendicular to both the velocity and the magnetic field, it demonstrates that in this electromagnetic interaction, the effect is perpendicular to its cause.

In this example, we consider a current-carrying wire placed in a magnetic field. When a current (I) flows through a wire of length (L) in the presence of a magnetic field (B), the wire experiences a magnetic force. This force, known as the magnetic Lorentz force, is given by the following equation: F = ILBsin(theta) where F is the magnetic force, I is the current, L is the length of the wire, B is the magnetic field, and theta is the angle between the current direction and the magnetic field direction. In this case, the cause of the electromagnetic interaction is the current flow (I) in the presence of the magnetic field (B), and its effect is the force (F) experienced by the wire. The sin(theta) term reflects that this force is maximum when the angle between the current and the magnetic field is 90 degrees (perpendicular) and minimum (zero) when they are parallel or anti-parallel. This shows that the effect of the electromagnetic interaction (force on the wire) is perpendicular to its cause (the current flow in the presence of the magnetic field).