Which of the following statements is/are true about Gaussian surfaces?

i. Gaussian surface is the name for a closed surfaces used when calculating flux in Gauss’ Law
ii. A Gaussian surface can have any shape (as long as it is closed)
iii. Like defining your system in energy problems, you can choose any shape or position of Gaussian surface in a problem
iv. It is easy to calculate flux with any Gaussian surfaces you choose
i only
i, ii, iii, and iv
i, ii, and iii only
i and ii only
i and iii only

It can have any shape BUT although it is easy to calculate E as a function of radius from a charge with a spherical surface where the E is constant over the surface and perpendicular to the surface, calculating the E field over the surface of a cube for example with a charge at the center would not be easy because it is not constant over the surface and is only perpendicular to the surface at the centers of the sides of the cube. iv is therefore totally false.

To determine which of the given statements are true about Gaussian surfaces, let's break down each statement individually.

i. Gaussian surface is the name for a closed surface used when calculating flux in Gauss' Law.

This statement is true. A Gaussian surface is a hypothetical closed surface that is used as a control surface in applying Gauss' Law to calculate electric flux. The electric flux through a closed Gaussian surface is directly related to the charge enclosed by that surface.

ii. A Gaussian surface can have any shape (as long as it is closed).

This statement is also true. The choice of the shape of the Gaussian surface is arbitrary, as long as it completely encloses the charge distribution of interest. This flexibility allows for easier calculations and simplification of the problem.

iii. Like defining your system in energy problems, you can choose any shape or position of Gaussian surface in a problem.

This statement is true as well. Similar to defining a system in energy problems, the choice of the shape or position of the Gaussian surface is based on convenience and making the calculations easier. It is important to select a Gaussian surface that simplifies the calculations, such as one that takes advantage of symmetry or simplifies the distribution of charges.

iv. It is easy to calculate flux with any Gaussian surface you choose.

This statement is not entirely true. While the use of a Gaussian surface simplifies the calculations of electric flux, the ease of calculating the flux depends on the complexity of the charge distribution and the chosen shape of the Gaussian surface. For more complex charge distributions, it may be challenging to find a suitable Gaussian surface that simplifies the calculations.

Based on the explanations above, the correct answer is "i, ii, and iii only".

The correct statement(s) about Gaussian surfaces are:

i. Gaussian surface is the name for a closed surface used when calculating flux in Gauss’ Law.

ii. A Gaussian surface can have any shape (as long as it is closed).

iii. Like defining your system in energy problems, you can choose any shape or position of Gaussian surface in a problem.

Therefore, the correct answer is i, ii, and iii only.