A sphere of radius 1 cm has potential of 8000 v, then energy density near its surface will be .

step 1 Hi friends here it is given a sphere of radius 1 cm having the potential 8 ,000 volt energy dens

A sphere of radius 1 cm has potential of 8000 v, then...

A sphere of radius $1 \mathrm{~cm}$ has potential of $8000 \mathrm{v}$, then energy density near its surface will be ...... (A) $64 \times 10^{5}\left(\mathrm{~J} / \mathrm{m}^{3}\right)$ (B) $2.83\left(\mathrm{~J} / \mathrm{m}^{3}\right)$ (C) $8 \times 10^{3}\left(\mathrm{~J} / \mathrm{m}^{3}\right)$ (D) $32\left(\mathrm{~J} / \mathrm{m}^{3}\right)$

A sphere of radius $1 \mathrm{~cm}$ has potential of $8000 \mathrm{v}$, then energy density near its surface will be ......
(A) $64 \times 10^{5}\left(\mathrm{~J} / \mathrm{m}^{3}\right)$
(B) $2.83\left(\mathrm{~J} / \mathrm{m}^{3}\right)$
(C) $8 \times 10^{3}\left(\mathrm{~J} / \mathrm{m}^{3}\right)$
(D) $32\left(\mathrm{~J} / \mathrm{m}^{3}\right)$

Key Concepts

Energy Density of an Electric Field

Energy density refers to the energy stored per unit volume in an electric field. It is calculated using the formula (1/2)??E², where ?? is the permittivity of free space and E is the electric field strength. This concept is vital in understanding how energy is distributed in space around charged objects.

Electric Potential

Electric potential is the amount of work needed per unit charge to move a charge from a reference point (typically infinity) to a specific point in an electric field. It is measured in volts and serves as a scalar representation of the energy landscape around charge distributions.

Electric Field

The electric field is a vector quantity that represents the force per unit charge experienced by a small test charge placed in the field. It is obtained as the spatial rate of change (gradient) of the electric potential and indicates both the magnitude and direction of the force, with units of volts per meter (V/m).

Relationship between Electric Potential and Electric Field

The electric field is directly related to the electric potential through the gradient operation. In regions where the potential changes rapidly, the electric field is strong. For instance, near the surface of a charged conductor, the potential’s rate of change is directly linked to the magnitude of the electric field at that surface.

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