Electrostatics

$\pi \frac{kq}{r^3}$

Zero

$2\pi \frac{kq}{r^3}$

$\frac{kq}{r^2}$

Their cross product with respect to local magnetic fields ($B \times r_{AB}$).

The divergence times distance squared between them ($\nabla \cdot E \times d^2$).

The dot product between their position vectors and the local electrical field intensity ($E \cdot r_{AB}$).

The difference in their electrical potentials ($V_A - V_B$).

2F

$\frac{F}{4}$

4F

$\frac{F}{2}$

$W_{ext} = qEd$, where $q$ is the particle's charge.

$W_{ext} = -q\Delta V$, with $\Delta V$ being the potential difference between two points.

$W_{ext} = 0$

$W_{ext} = Fd$

It halves.

It quadruples.

It remains unchanged.

It doubles.

Toward the point charge.

Away from the point charge.

It has no specific direction and is random.

In a circular path around the point charge.

A cylindrical surface coaxial with the line charge

A spherical shell centered around any point along length of line charge

An elliptical cylinder with major axis along direction perpendicular to line charge

A square loop perpendicular to and centered on the line charge

$-12xy \ \mathrm{m/s^2} \ \mathbf{i} +18z \ \mathrm{m/s^2} \ \mathbf{j} +8 \ \mathrm{m/s^2} \ \mathbf{k}$

$-6 \times 10^{14} \ \mathrm{m/s^2} \ \mathbf{i} +9 \times 10^{14} \ \mathrm{m/s^2} \ \mathbf{j} -16 \times 10^{14} \ \mathrm{m/s^2} \ \mathbf{k}$

$-6x \ \mathrm{m/s^2} \ \mathbf{i} +9y \ \mathrm{m/s^2} \ \mathbf{j} -18z \ \mathrm{m/s^2} \ \mathbf{k}$

$-9.11 \times 10^{14} \ \mathrm{m/s^2} \ \mathbf{i} + 6.07 \times 10^{14} \ \mathrm{m/s^2} \ \mathbf{j} -18 \times 10^{14} \ \mathrm{m/s^2} \ \mathbf{k}$

It decreases.

It oscillates between high and low values.

It remains constant.

It increases.

It exerts an electrical force on it.

It increases its mass.

It nullifies gravitational forces on it.

It changes its color spectrum emission.