Force on a Charge: Electric and Magnetic Fields | 电荷在电场与磁场中所受的力

📚 Force on a Charge: Electric and Magnetic Fields | 电荷在电场与磁场中所受的力

In A-Level Physics, a charged particle experiences forces in electric and magnetic fields. Electric fields exert a force on any charge, while magnetic fields only exert a force on a moving charge. Understanding these forces is essential for topics such as particle accelerators, mass spectrometers, velocity selectors and the Hall effect.

在 A-Level 物理中，带电粒子在电场和磁场中会受到力的作用。电场对任何电荷都施加力，而磁场只对运动电荷施加力。理解这些力对于粒子加速器、质谱仪、速度选择器和霍尔效应等主题至关重要。

1. Electric Force in an Electric Field | 电场中的电场力

Electric field strength E is a vector quantity defined as the electric force per unit positive charge placed at that point. Therefore, a point charge q in an electric field E experiences a force given by:

电场强度 E 是矢量，定义为单位正电荷在电场中所受的电场力。因此，电场 E 中的点电荷 q 所受到的力为：

F = qE

If the electric field is uniform, the force is constant in both magnitude and direction. For a positive charge, the force is in the same direction as E; for a negative charge, the force is opposite to E.

如果电场是匀强电场，力的大小和方向都保持不变。对于正电荷，力的方向与 E 相同；对于负电荷，力的方向与 E 相反。

Electric field strength can also be written in volts per metre, V m⁻¹. In a parallel-plate system with potential difference V and plate separation d, the force on a charge is F = qV/d.

电场强度也可以用伏特每米（V m⁻¹）表示。在电势差为 V、板间距为 d 的平行板系统中，电荷所受的力为 F = qV/d。

2. Coulomb’s Law for Point Charges | 点电荷之间的库仑力

Coulomb’s law describes the force between two stationary point charges. The force is proportional to the product of the charges and inversely proportional to the square of their separation.

库仑定律描述两个静止点电荷之间的力。该力与两个电荷的乘积成正比，与它们之间距离的平方成反比。

F = q₁q₂ / (4πε₀ r²)

The constant 1/(4πε₀) is approximately 8.99 × 10⁹ N m² C⁻² in a vacuum. The force is repulsive for like charges and attractive for unlike charges, and it acts along the line joining the two charges.

真空中常数 1/(4πε₀) 约等于 8.99 × 10⁹ N m² C⁻²。同种电荷相互排斥，异种电荷相互吸引，力的方向沿两电荷的连线。

Coulomb’s law is an inverse-square law, similar in form to Newton’s law of gravitation, but the electrostatic force between charged particles is much stronger than the gravitational force between them.

库仑定律是平方反比定律，形式与牛顿万有引力定律相似，但带电粒子之间的静电力远大于它们之间的引力。

3. Magnetic Force on a Moving Charge | 运动电荷在磁场中的磁力

A magnetic field exerts a force on a charged particle only when the particle is moving. For a charge q moving at speed v at an angle θ to the magnetic field B, the magnitude of the magnetic force is:

磁场只对运动电荷施加力。对于以速度 v 运动、且速度方向与磁场 B 成 θ 角的电荷 q，磁力的大小为：

F = Bqv sinθ

The force is maximum when the velocity is perpendicular to the magnetic field, because θ = 90° and sinθ = 1. The force is zero when the velocity is parallel to the field, since θ = 0° or 180° and sinθ = 0.

当速度方向与磁场垂直时，θ = 90°，sinθ = 1，力最大。当速度方向与磁场平行时，θ = 0° 或 180°，sinθ = 0，力为零。

For a negative charge, use the magnitude of q in F = Bqv sinθ, but the direction of the force reverses. The SI unit of magnetic field strength B is the tesla, T

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