A metal sphere with 1 m radius and a surface charge density of 10 coulombs/$m^2$ is enclosed in a cube of 10 m side. The total outward electric displacement flux normal to the surface of the cube is:
$40 \pi$ coulombs
Flux Calculation Using Gauss's Law
The problem asks for the total outward electric displacement flux normal to the surface of a cube that encloses a charged metal sphere. According to Gauss's Law for electric displacement, the total outward flux ($D_{flux}$) through a closed surface is equal to the total charge enclosed ($Q_{enc}$) within that surface.
The formula is given by: $ D_{flux} = \oint \vec{D} \cdot d\vec{A} = Q_{enc} $
Enclosed Charge Calculation
First, calculate the total charge ($Q_{enc}$) on the metal sphere. The sphere has a radius ($R$) of 1 m and a surface charge density ($\sigma$) of 10 C/$m^2$. The surface area ($A$) of the sphere is calculated as:
$ A = 4 \pi R^2 $Substituting the given radius:
$ A = 4 \pi (1 \text{ m})^2 = 4 \pi \text{ m}^2 $Now, calculate the total charge enclosed:
$ Q_{enc} = \sigma \times A $ $ Q_{enc} = (10 \text{ C/m}^2) \times (4 \pi \text{ m}^2) $ $ Q_{enc} = 40 \pi \text{ C} $Determining Total Electric Displacement Flux
Since the cube encloses the charged sphere, the total outward electric displacement flux normal to the surface of the cube is equal to the total charge enclosed by the sphere.
$ D_{flux} = Q_{enc} $ $ D_{flux} = 40 \pi \text{ C} $The side length of the cube (10 m) is irrelevant for calculating the total flux as long as it completely encloses the sphere.
Final Answer
The total outward electric displacement flux normal to the surface of the cube is $40 \pi$ coulombs.
Similar Questions
Match List - I with List - II.
List - I (Laws) List - II (Applications) A. Ampere's law I. Force on a charge B. Biot's law II. Force due to a current carrying conductor C. Coulomb's law III. Electric flux density at a point D. Gauss's law IV. Magnetic flux density at a point - DNS is primarily used for:
The pointing vector $P = E \times H$ represents:
- Arrange these digital logic building blocks in order of increasing complexity:
A. Multiplexers
B. Sequential logic circuits e.g.: counters
C. Combinational logic circuits e.g.: adder
D. ALU (Arithmetic Logic Unit)
Choose the correct answer from the options given below: - Signal flow graph is used to find:
- Consider the following frequency domain specifications required to design a control system:
A. Bandwidth
B. Gain margin
C. Phase margin
D. Maximum overshoot
Choose the correct answer from the options given below: A-network connected with its Y-equivalent is shown in figure. Find the resistance $R_1$, $R_2$ and $R_3$ are respectively:
Match List - I with List - II.
List - I (Compensation) List - II (Characteristics) A. Lead I. Attenuation B. Lag II. Increases bandwidth C. Lag-lead III. Increases damping faster D. Rate IV. Second order - Which protocol in the TCP/IP suite is responsible for breaking data into packets and reassembling them at the destination providing reliable, connection-oriented delivery?
Match List - I with List - II.
List - I (Communication System) List - II (Bandwidth) A. AM broadcast I. 7 MHz B. Telephone II. 200 KHz C. Wideband FM III. 4 KHz D. TV IV. 10 KHz
Important Questions from Mixed Topic (CUET PG)
- Who was the founder of Bolshevik Communist party?
- What is the key guide to statecraft in the realist tradition?
- Chronologically arrange the events in the Cold War period.
A. Berlin Wall is constructed
B. Communist China joins the UN
C. Soviet invasion of Czechoslovakia
D. Berlin Blockade
Choose the correct answer from the options given below: Morgenthau's principles of political realism are:
A. Politics is rooted in permanent and unchanging human nature which is basically self centred, self-regarding and self-interested
B. Politics is an autonomous sphere of action and cannot therefore be reduced to morals
C. International Politics is an arena of conflicting self-interests
D. The ethics of international relations is situational ethics which is very different from private morality
Choose the correct answer from the options given below:Who among the following political thinkers consider the anarchical self help system to be a compelling factor for States to maximise their relative power positions?
