Xhangest law provide a method us alculate ary alection Thend Mish sh application in fields of inghly symmetric sistributesem ar in wat changess
8. In dianing electric ficid lines for any static configuration of charmes. shac inch and terminare on charges $A,+\cdots+13,+4,+1) \ldots$
9. The electric field is defined as the force post unif change exerast on a samiliss
$\frac{ kg _2 g_2}{r^3}$
D. $F=\frac{4 \times 92}{4 \pi a^2}$
10. The lmaginary surface necessary to apply Cuuss law is called Bipolar Surface
Q. Ciaussian Surface
1. None of the above
1. If the surface under consideration is not perpendicular to the fista line, une given as $A, \Sigma B A \cos 0$
3. $2 E A \cos \pi C \quad 2 E \cos \theta \quad D \quad 2 . A \cos \theta$
7. What is the integral form of the cxpression 2 , EA cos $0=\frac{0}{0}$ :
A. 5
$P f E \cdot A=\frac{Q}{\varepsilon_s}$
$C \cdot \int A \cdot d E=\frac{1}{B a}$
1). $\int E / A=\frac{0}{4 a}$
Answer (2)
Gauss's law relates electric flux through a closed surface to the enclosed charge.
The integral form of Gauss's law is expressed as ∮ E ⋅ d A = ϵ 0 Q .
Option B, ∮ E ⋅ A = ε 0 Q , matches the integral form of Gauss's law.
Therefore, the correct answer is B .
Explanation
Problem Analysis We are asked to identify the integral form of the expression related to Gauss's law. Gauss's law relates the electric flux through a closed surface to the enclosed electric charge. The electric flux is given by the surface integral of the electric field over the closed surface.
Gauss's Law in Integral Form Gauss's law in integral form is given by:
The Formula ∮ E ⋅ d A = ϵ 0 Q
Explanation of variables where:
E is the electric field,
d A is the differential area vector,
Q is the enclosed charge,
ϵ 0 is the permittivity of free space.
Finding the Correct Option Comparing the given options with the integral form of Gauss's law, we look for an expression that matches the form ∮ E ⋅ d A = ϵ 0 Q .
The Answer Option B, ∮ E ⋅ A = ε 0 Q , is the correct integral form of Gauss's law.
Examples
Gauss's law is fundamental in electromagnetism and is used in various applications, such as calculating the electric field due to symmetric charge distributions, designing capacitors, and understanding the behavior of electromagnetic waves. For instance, in designing a coaxial cable, Gauss's law helps determine the electric field between the inner and outer conductors, which is crucial for calculating the cable's capacitance and impedance. This ensures the cable transmits signals efficiently with minimal loss.
Gauss's law relates the electric flux through a closed surface to the enclosed charge, expressed as ∮ E ⋅ d A = ϵ 0 Q . Among the provided options, Option B is the correct integral form of Gauss's law: ∮ E ⋅ A = ε 0 Q . This law is vital for calculating electric fields in symmetric charge distributions.
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