Superposición electrostática, flujo y conductores
GRE Subject Test · GRE Physics Tema 13 5:27 Narración en inglés · Subtítulos en inglés + 中文 quemados en pantalla
Capítulos
Transcripción
A charged conductor can have zero field inside its material while its potential is not zero.
带电导体内部的电场可以为零，而它的电势却不为零。
This topic adds Coulomb forces as vectors using the real geometry, finds flux from symmetry or solid angle, and finds conductor fields and potentials from the induced surface charges.
本主题按实际几何把库仑力作为矢量相加，用对称性或立体角求通量，并由感应表面电荷求导体的电场和电势。
For a point charge Q at position r 0, the field E at r equals Q times the vector r minus r 0, divided by 4 pi epsilon nought times the magnitude of r minus r 0, cubed.
对于位于 r0 处的点电荷 Q，r 处的电场等于 Q 乘以矢量 r 减 r0，再除以 4π ε0 乘以 r 减 r0 的模的立方。
Superpose vectors, not field magnitudes.
叠加的是矢量，而不是场强大小。
For two positive charges attracting an electron, forces in the same direction add; opposite directions subtract; perpendicular components combine by Pythagoras.
两个正电荷吸引一个电子时，同向的力相加，反向的力相减，垂直分量按勾股定理合成。
Define the observation point and the direction of each force first.
先确定观测点和每个力的方向。
Potential is the scalar sum V equals the sum of Q over 4 pi epsilon nought r, with zero at infinity.
电势是标量和，V 等于各个 Q 除以 4π ε0 r 之和，取无穷远处为零。
A zero potential does not generally mean a zero field, since E equals minus the gradient of V.
电势为零一般不代表电场为零，因为 E 等于负的 V 的梯度。
Gauss's law is the closed-surface integral of E dot d A equals Q enclosed divided by epsilon naught.
高斯定律是闭合曲面积分，E点乘dA等于Q enclosed除以epsilon naught。
It determines a local field simply only when symmetry makes the normal field uniform or makes other flux contributions zero.
它仅在对称性使法向场均匀或使其他通量贡献为零时，才能简单地确定局部场。
A charge near an infinite plane sends half its total flux through that plane in magnitude, because the plane subtends solid angle 2 pi out of 4 pi.
一个电荷靠近无限大平面时，其总通量的一半以该平面的大小通过；这是因为该平面所张立体角为2 pi，而全空间为4 pi。
The result is independent of distance and lateral position, but its sign depends on the chosen plane normal and charge sign.
结果与距离和侧向位置无关，但其符号取决于所选平面法向及电荷符号。
An open plane does not enclose a charge; using closed-surface wording for it is incorrect.
开放平面不包围电荷；对其使用闭合曲面表述是不正确的。
In electrostatic equilibrium, the electric field inside conducting material is zero and the conductor has constant potential.
在静电平衡状态下，导体材料内部电场为零，导体为等势体。
Place a charge Q at the centre of a conducting spherical shell with inner radius a, outer radius b and shell net charge q.
将电荷 Q 放在内半径为 a、外半径为 b、净电荷为 q 的导体球壳中心。
A Gaussian surface inside the material requires an inner-surface charge of minus Q, so the outer surface has q plus Q.
材料内部的高斯面要求内表面电荷为负 Q，因此外表面电荷为 q 加 Q。
Spherical symmetry makes the external field that of the total Q plus q at the centre.
球对称使外部电场等同于位于中心的总电荷 Q 加 q 的电场。
The material's potential, zero at infinity, is Q plus q over 4 pi epsilon nought b, independent of the material observation radius.
取无穷远为零，导体材料的电势等于 Q 加 q 除以 4π ε0 b，与在材料内的观测半径无关。
In the cavity of that centred-charge shell, the field is Q over 4 pi epsilon nought r squared, radially, for r between 0 and a.
在这个中心带电的球壳空腔内，当 r 介于 0 和 a 之间时，电场沿径向，大小为 Q 除以 4π ε0 r 平方。
Potential includes both the point-charge contribution and constant shell contributions; continuity holds across each surface even though the normal field jumps at a surface charge.
电势包括点电荷的贡献和球壳的常数贡献；尽管面电荷处法向电场发生跃变，电势在每个表面上仍然连续。
Keep cavity, conductor material and exterior separate.
要把空腔、导体材料和外部区域分开处理。
An off-centre charge still induces a total inner charge of minus Q, but its cavity field is no longer the simple centred radial field.
偏心电荷仍会在内表面感应出总电荷负 Q，但空腔内的电场不再是简单的中心径向场。
Zero interior conductor field follows from equilibrium, not from an assumption that every surface charge distribution is uniform.
导体内部电场为零来自平衡条件，而不是假设每个面电荷分布都均匀。
Take Q equal to plus 2 nanocoulombs and q equal to minus 1.
取 Q 等于正 2 纳库，q 等于负 1 纳库。
The inner surface carries minus 2 and the outer surface plus 1 nanocoulomb.
内表面带负 2 纳库，外表面带正 1 纳库。
The metal's potential is k times q plus Q over b: 9 times 10 to the 9, times 1 times 10 to the minus 9, over 0.30 metres, which is 30 volts.
金属的电势等于 k 乘 q 加 Q 再除以 b：9 乘 10 的 9 次方，乘 1 乘 10 的负 9 次方，除以 0.30 米，等于 30 伏。
The cavity is not metal, so its field need not vanish.
空腔不是金属，所以其中的电场不必为零。
Move Q away from the centre while keeping it inside the closed cavity.
将Q移离中心，同时保持其位于封闭空腔内部。
The shell's exterior remains a sphere, with no external charges.
壳层外部仍为球面，且无外部电荷。
Which of inner charge total, inner charge distribution, metal potential and exterior field retain their centred values?
内表面总电荷、内表面电荷分布、金属电势和外部场中，哪些量能保持居中时的数值？
Explain using Gauss's law and electrostatic uniqueness.
请利用高斯定律和静电唯一性定理进行解释。
The inner total remains negative Q because the metal field stays zero, but its distribution is generally nonuniform.
内部总电荷仍为负Q，因为金属内部场强保持为零，但其分布通常是非均匀的。
Outer total remains q plus Q.
外部总电荷仍为q加Q。
The spherical exterior is equipotential. Uniqueness with zero at infinity gives V equals k times q plus Q, all over r, outside.
球面外部是等势体；结合无穷远处电势为零的唯一性定理，外部电势V等于k乘以q加Q除以r。
So metal potential and exterior field retain their centred values.
因此，金属的电势和外部电场保持其中心对称值不变。 但空腔内的电场会发生变化。
Cavity field changes. Award inner total, redistribution, outer total, uniqueness argument, and unchanged exterior potential.
评分要点包括：内部总电荷、重新分布、外部总电荷、唯一性论证，以及外部/电势保持不变。
Do not confuse the open-plane half-flux result with enclosed charge.
请勿将开放平面的半通量结果与包围电荷混淆。
A conductor’s zero field fixes a constant potential, not necessarily zero potential.
导体内场强为零意味着电势为常数，但不一定为零。
solid angle: Angular area subtended by a surface, measured in steradians.
立体角：由曲面所张开的角面积，单位为球面度。
induced surface charge: Charge rearranged on a conductor to satisfy electrostatic equilibrium.
感应表面电荷：为使导体达到静电平衡而在其表面重新分布的电荷。
Retrieve the meanings without reading the definitions, then change a parameter in the original transfer and test the limiting case.
在不阅读定义的情况下回忆其含义，然后改变原始传递中的一个参数，并检验极限情况。