Question

At any point in space, the electric field$\overrightarrow{\mathbf{E}}$is defined to be in the direction of the electric force on a positively charged particle at that point. Why don’t we similarly define the magnetic field$\overrightarrow{\mathbf{B}}$to be in the direction of the magnetic force on a moving, positively charged particle?

Short answer

Electric force on a charged particle has a fixed direction. It can be determined as the direction of the electric force on a charged positively charged particle

Step-by-step solution

Direction of electric force on a charged particle

The electric force on a charge particle has a fixed direction which depends only on the nature of the charge and the direction of the electric field. Therefore, the direction of the electric field can be defined as the direction of the electric force on a positively charge particle. The magnetic force acting on a charged particle however, depends on the direction in which the particle is moving. In fact, the magnetic force is perpendicular to the velocity of the charged particle and the direction of the magnetic field. Hence, it cannot be defined the direction of the magnetic field as the direction of the force acting on the charged particle

Conclusion

Therefore, the electric force on a charged particle has a fixed direction which depends only on the sign of the charge and the direction of the electric field. Hence the direction of the electric field can be defined as the direction of the electric force on a positively charged particle.

Again, the magnetic force is perpendicular to both the velocity of the charged particle and the direction of the magnetic field. The direction of the magnetic force will be different. Hence we cannot define the direction of the magnetic field as the direction of force acting on the charged particle.