Question

Match List-I with List-II. List-I (Laws): 
• A. Ampere’s law 
• B. Biot-Savart law 
• C. Coulomb’s law 
• D. Gauss’s law 

List-II (Applications): 
• I. Force on a charge 
• II. Force due to a current carrying conductor 
• III. Electric flux density at a point 
• IV. Magnetic flux density at a point

• A. A-I, B-II, C-III, D-IV
• B. A-IV, B-II, C-I, D-III
• C. A-III, B-II, C-I, D-IV
• D. A-II, B-I, C-III, D-IV

Hint:

Remember: Coulomb → Force between charges, Biot-Savart → Magnetic field due to current, Ampere → Magnetic flux, Gauss → Electric flux.

Answer 1

The Correct Option is B

Concept: Each physical law describes a specific electromagnetic phenomenon and is associated with a particular application:
• Ampere’s Law: Relates magnetic field to current.
• Biot-Savart Law: Calculates magnetic field due to a current element.
• Coulomb’s Law: Determines force between electric charges.
• Gauss’s Law: Relates electric flux to enclosed charge.

Step 1: Match Ampere’s Law Ampere’s law gives the relationship between current and magnetic field: \[ \oint \vec{B} \cdot d\vec{l} = \mu_0 I \] It is used to determine magnetic flux density. \[ A \rightarrow IV \]

Step 2: Match Biot-Savart Law Biot-Savart law gives the magnetic field due to a small current element: \[ d\vec{B} \propto \frac{I \, d\vec{l} \times \hat{r}}{r^2} \] It is used for calculating effects due to current-carrying conductors. \[ B \rightarrow II \]

Step 3: Match Coulomb’s Law Coulomb’s law gives force between charges: \[ F = k \frac{q_1 q_2}{r^2} \] \[ C \rightarrow I \]

Step 4: Match Gauss’s Law Gauss’s law: \[ \oint \vec{E} \cdot d\vec{A} = \frac{Q}{\epsilon_0} \] It is used to determine electric flux density. \[ D \rightarrow III \]

Step 5: Final matching \[ A-IV,\quad B-II,\quad C-I,\quad D-III \] \[ \therefore \text{Correct answer is (B)} \]