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Current Question (ID: 16473)
Question:
$\text{Given below are two statements:}$ $\text{Statement I:}$ $\text{Gauss's law for electric fields is a consequence of the conservation of energy.}$ $\text{Statement II:}$ $\text{Coulomb's law for electric charges leads to a conservative electric field.}$
Options:
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1. $\text{Statement I is incorrect and Statement II is correct.}$
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2. $\text{Both Statement I and Statement II are correct.}$
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3. $\text{Both Statement I and Statement II are incorrect.}$
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4. $\text{Statement I is correct and Statement II is incorrect.}$
Solution:
$\text{Hint: The electrostatic field is a conservative field.}$ $\text{Explanation: Gauss' law concerns the electric flux. It is in no way connected to the conservation of energy.}$ $\text{The electric flux through a closed surface to the charge enclosed.}$ $\text{Gauss's law is a direct consequence of Coulomb's law and is derived using the concept of field lines spreading radially from a charge.}$ $\text{It is a mathematical restatement of the inverse square law, which relates to charge distribution.}$ $\text{It has no direct connection with the conservation of energy.}$ $\text{Conservation of energy applies to the work done by the field, but Gauss's law arises from the symmetry of electric fields, not energy conservation.}$ $\text{The electric field produced by a charge is conservative because the work done by the field is path-independent.}$ $\text{This is a key property of conservative fields.}$ $\text{Coulomb's law directly implies a conservative electric field which means the electric field has no curl.}$ $\text{Every central force is a conservative force and the Coulomb force is also a conservative force.}$ $\text{Hence, option (1) is the correct answer.}$
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