Question

Which of the following statements correctly describes the Biot Savart's law and its applications
• The magnetic field \(dB\) from a current element is directly proportional to the current \(I\)
• The magnetic field is inversely proportional to the square of the distance
• It helps to determine the electric field around a stationary charge
• It is used to find the magnetic field at the center of a circular current loop Choose the correct answer from the options given below:

• A. A, B & D Only
• B. A, B, C & D Only
• C. A, B & C Only
• D. A & B Only

Hint:

Biot-Savart law: \[ dB\propto \frac{I\,dl\sin\theta}{r^2} \] It is used to calculate magnetic fields due to current carrying conductors.

Answer 1

The Correct Option is A

Concept: Biot-Savart law gives the magnetic field produced by a small current carrying element. It is one of the fundamental laws of magnetostatics. The law states: :contentReference[oaicite:1]{index=1} where:
• \(I\) = current
• \(dl\) = current element
• \(r\) = distance from observation point
• \(\theta\) = angle between \(dl\) and position vector

Step 1: Analyze Statement A. From Biot-Savart law: \[ dB \propto I \] Thus:
• Increasing current increases magnetic field. Hence Statement A is correct.

Step 2: Analyze Statement B. From the formula: \[ dB \propto \frac{1}{r^2} \] Therefore magnetic field decreases with square of distance. Hence Statement B is correct.

Step 3: Analyze Statement C. Statement C says: “It helps to determine electric field around a stationary charge” This is incorrect because:
• Biot-Savart law deals with magnetic fields.
• Electric field around stationary charges is determined using Coulomb's law. Hence Statement C is incorrect.

Step 4: Analyze Statement D. Biot-Savart law is commonly used to calculate:
• Magnetic field at center of circular current loop
• Magnetic field due to straight conductor
• Magnetic field due to arcs Thus Statement D is correct.

Step 5: Determine correct combination. Correct statements: \[ A,\ B,\ D \] Incorrect statement: \[ C \] Therefore: \[ \boxed{ A,\ B\ \&\ D\ \text{Only} } \]

Step 6: Choose the correct answer. Hence the correct option is: \[ \boxed{(1)} \] Final Conclusion: Biot-Savart law:
• Relates magnetic field with current element
• Varies inversely as square of distance
• Is used to calculate magnetic fields of current carrying conductors Hence, the correct answer is: \[ \boxed{(1)} \]