## Explanation

### Introduction

In a simple electric motor, various energy transformations occur to convert electrical energy into mechanical energy, which drives the motor's motion. Understanding these transformations is crucial for grasping the motor's functionality.

### Energy Input

The process begins with the input of **electrical energy**. This energy is supplied by a power source, such as a battery or a power grid, which drives the electric current through the motor's components.

### Electromagnetic Interaction

The supplied electrical energy results in current flow through the motor's wire coils, generating a **magnetic field** according to Ampere's Law:

Where:

- $\vec{B}$ is the magnetic field.
- $\mu_0$ is the permeability of free space.
- $I$ is the current.
- $r$ is the radius of the loop.

### Mechanical Work

The interaction between the generated magnetic field and the permanent magnets inside the motor creates a **magnetic force**. This force produces **torque** on the motor's shaft, leading to its rotation as described by the formula:

Where:

- $\tau$ is the torque.
- $r$ is the radius from the axis of rotation.
- $F$ is the magnetic force.
- $\theta$ is the angle between the force and the lever arm.

### Energy Conversion

The motor converts **electrical energy** into **kinetic energy** (the energy of motion) and **mechanical energy** as the rotor turns. This transformation can be summarized with the equation:

Where:

- $P_{mech}$ is the mechanical power output.
- $P_{elec}$ is the electrical power input.
- $P_{loss}$ represents energy losses (e.g., due to friction, heat).

### Heat Generation

During the energy conversion process, some energy is inevitably lost due to **resistance** in the motor's coils, leading to **heat** production. This can be quantified as:

Where:

- $Q$ is the heat energy.
- $I$ is the current.
- $R$ is the resistance.
- $t$ is the time for which the current flows.

### Conclusion

In summary, a simple electric motor primarily transforms electrical energy into mechanical energy through electromagnetic interactions, resulting in the rotor's rotation. Some energy is also inevitably converted into heat due to internal resistance. These transformations underscore the principle of energy conservation and the efficiency of electric motors in mechanical applications.