Notes from Toppers
Magnetostatics and BiotSavart’s Law  JEE Topper’s Notes
Key Points:
 Basic Concepts of Magnetostatics:
 Magnetic Field: –Definition: A region around a currentcarrying conductor or a magnet where its influence can be felt is known as a magnetic field. –Representation: It is represented by vectors known as magnetic field lines which indicate the direction and strength of the magnetic field.
 BiotSavart Law (NCERT Reference: Class 12 Physics, Chapter 4)
 Mathematical formula to calculate the magnetic field at a point due to a differential currentcarrying element.
 The direction of the magnetic field at a point due to a current element is given by the righthand thumb rule.
 The magnitude of the magnetic field is directly proportional to the current and inversely proportional to the square of the distance from the current element.
 Magnetic Field due to:

Straight CurrentCarrying Wire: –Applying BiotSavart’s law, the magnetic field at a distance ‘r’ from a long straight wire carrying current ‘I’ is given by: – $$ B = \frac{\mu_0}{4\pi} \frac{2I}{r} $$ where (\mu_0) is the permeability of free space.

Circular Loop: –At the center of a circular loop of radius ‘R’ carrying current ‘I’, the magnetic field is given by: – $$B = \frac{\mu_0I}{2R} $$ – On the axis of the circular loop, the magnetic field at a distance ‘x’ from the center is given by: –$$B = \frac{\mu_0I}{4\pi}\left(\frac{R^2}{(R^2+x^2)^{3/2}}\right)$$
 Magnetic Field due to Solenoids (NCERT Reference: Class 12 Physics, Chapter 5)
 A solenoid is a long cylindrical coil of wire closely wound in the form of a helix.
 The magnetic field inside a solenoid is uniform and is given by: –$$B = \mu_0nI$$ where (n) is the number of turns per unit length of the solenoid.
 Applications of BiotSavart Law:
 Magnetic Dipole: – A current loop acts like a magnetic dipole, with its north pole pointing in the direction of the magnetic field at its center. – The magnetic dipole moment of a current loop is given by: –$$ m=IA$$ where I is the current and A is the area of the loop.
 Torque on CurrentCarrying Loop in Magnetic Field: –When a currentcarrying loop is placed in a magnetic field, it experiences a torque given by: – $$\overrightarrow \tau = \overrightarrow m\times \overrightarrow B$$ where ( \overrightarrow m ) is the magnetic moment of the loop and ( \overrightarrow B ) is the external magnetic field.
 Ampere’s law (NCERT Reference: Class 12 Physics, Chapter 4)
 Ampere’s law is a generalization of BiotSavart’s law and states that the line integral of magnetic field around a closed loop is equal to the total current passing through the surface bounded by the loop.
 $$ \oint \overrightarrow B \cdot d\overrightarrow l = \mu_0\sum I_{enc} $$ where ( \mu_0) is the permeability of free space, ( I_{enc} ) represents the net current flowing through the surface enclosed by the loop.
 Ampere’s law is particularly useful in determining the magnetic field due to symmetric current distributions.
 Solved Problems and Numerical Practice:
 Practice a wide range of solved examples and numerical problems based on the concepts and equations discussed above to reinforce understanding and hone problemsolving skills.
Reference:
 NCERT Physics Class 11 and 12, CBSE