# Biot-Savart Law Numericals

Last updated on August 23rd, 2023 at 10:45 am

Physics Numerical Problems Based on Biot Savart Law– The Biot-Savart law is a fundamental relationship in magnetostatics. It describes the magnetic field generated by a steady current. In this post, we will look at a set of numerical problems based on the Biot-Savart law and their step-by-step solutions.

**Formulas Used**

The Biot-Savart law allows us to calculate the magnetic field B at some point P due to a current-carrying conductor. It states that:

dB = (μ_{0}/4π) (I**dl **x **r**)/r^3

Where:

dB is the incremental magnetic field at point P

μ_{0}is the permeability of free space

I is the current in the conductor

dl is an incremental length of the conductor

r is the displacement vector from dl to P

To find the total magnetic field B, we integrate dB over the entire length of the conductor.

**Biot-Savart Law Numericals (class 12)**

Below are 10 numerical problems based on the Biot Savart law.

Problem 1: Calculate the magnetic field at point P located on the axis at a distance of 10 cm from the center of a circular wire of radius 5 cm carrying a current of 5 A.

**Solution**: [Biot-Savart numerical set1 Q1 Solution]

Problem 2: Find the magnetic field at a distance of 20 cm from a long, straight wire carrying a current of 10A.

Solution: [Biot-Savart-numerical set1 Q2 solution]

Problem 3: Calculate the magnetic field at the center of a square loop of side 10 cm carrying a current of 5A.

Solution: [Q3 Solution]

Problem 4: Find the magnetic field at a point on the axis of a circular coil of 100 turns and a radius of 10 cm carrying a current of 1.5A at a distance of 15cm from the center.

Problem 5: Calculate the magnetic field at the center of a square of side 30 cm carrying a current of 15A along each arm.

Problem 6: Find the magnetic field at a distance of 5cm from an infinitely long straight conductor carrying a current of 8A.

Problem 7: Calculate the magnetic field at a point on the axis at a distance of 12cm from the center of a circular loop of radius 8cm carrying a current of 3A.

Problem 8: A square conducting loop of side length L carries a current I. The magnetic field at the center of the loop is:

A) independent of L

B) proportional to L

C) inversely proportional to L

D) linearly proportional to L

Hint: B∝1/L

problem 9: A current-carrying wire is in the form of a square loop of side length 25 cm. The current in the wire is 2A. Find out the magnetic field at the center of the loop.

problem 10: The magnetic induction at the center of a current-carrying circular coil of radius 10 cm is

5.5^{1/2} times the magnetic induction at a point on its axis. The distance of the point from the center of the coil in cm is:___________________