A conducting sphere \(18 \mathrm{~cm}\) in diameter is charged to \(9 \mathrm{kV}\) above earth potential and isolated. Find the charge on the sphere, the E-field just outside it and the field and potential \(18 \mathrm{~cm}\) from its centre.

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electric field. Charges come in two types: positive and negative. Like charges repel, while opposite charges attract. The smallest unit of charge is carried by subatomic particles—with electrons bearing a negative charge and protons a positive one.

Charged objects influence each other through the electric force, and this interaction is crucial in determining the behavior of charged objects, such as the conducting sphere in our exercise. The sphere's ability to hold an electric charge allows it to create an electric field around it and exhibit an electric potential relative to another point, such as the earth in this case.

Coulomb's law is a principle that quantifies the electric force between two point charges. The law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. It can be expressed mathematically as:
\[F = k\frac{|q_1 q_2|}{r^2}\]
where \(F\) is the force, \(k\) is Coulomb's constant (\(8.9875\times10^9\) Nm²/C²), \(q_1\) and \(q_2\) are the charges, and \(r\) is the distance between the charges. In our exercise, Coulomb's law helps to determine the charge on the sphere by relating it to the known potential and radius.

Electric potential is a measure of the potential energy per unit charge at a point in an electric field. It represents the work done to move a small positive test charge from a reference point to the specific point without creating acceleration. For a charged sphere, the electric potential (V) at a distance (r) from its center can be calculated using:
\[V = \frac{kQ}{r}\]
where \(V\) is the potential, \(k\) is Coulomb's constant, \(Q\) is the total charge on the sphere, and \(r\) is the distance from the sphere's center. In simple terms, it tells us how much electric energy is stored in the sphere's field at a certain distance. As the exercise improvement suggests, it’s essential to clarify that the potential outside the sphere decreases with radius—an important concept for students to understand when studying electric fields.