TO DRAW THE MAGNETIC LINES OF FORCE DUE TO A BAR MAGNET

To trace the magnetic lines of force around a Bar Magnet and to locate the neutral points.

• A bar magnet
• A magnetic compass
• Drawing board
• Drawing sheet (white paper)
• Drawing pins or adhesive tape
• Pencil (HB)
• Scale and protractor

A magnet is surrounded by a magnetic field that exerts forces on other magnetic materials or moving charges. This field can be represented by magnetic lines of force, which are imaginary lines used to visualize the direction and strength of the magnetic field.

The magnetic lines of force have the following properties:

• They originate from the north pole and terminate at the south pole of the magnet.
• The tangent to a field line at any point gives the direction of the magnetic field at that point.
• The density of the lines indicates the strength of the magnetic field; closer lines mean a stronger field.
• The lines never intersect each other.
• Outside the magnet, they travel from north to south pole, while inside the magnet, they travel from south to north pole, forming closed loops.

The magnetic field at any point due to a bar magnet can be represented mathematically. For a point at a distance $r$ from the center of a magnet making an angle $\theta$ with the axis of the magnet, the magnetic field has two components:

where $B_r$ is the radial component, $B_\theta$ is the transverse component, $\mu_0$ is the permeability of free space, and $M$ is the magnetic moment of the bar magnet.

Neutral Points: These are points in the magnetic field where the resultant field is zero. For a bar magnet, they are located along the axial line and equatorial line, where the magnetic field of the magnet exactly cancels the earth's magnetic field.

The magnetic field at a distance $r$ from the center of a magnetic dipole of moment $M$ is given by:

Where:

• $B$ is the magnetic field strength at the point
• $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7}$ H/m)
• $M$ is the magnetic moment of the bar magnet
• $r$ is the distance from the center of the magnet to the point of observation
• $\theta$ is the angle made by the line joining the center of the magnet and the point of observation with the axis of the magnet

For the axial line ($\theta = 0°$ or $180°$):

For the equatorial line ($\theta = 90°$):

1. Preparation:
   • Fix a white paper on the drawing board using drawing pins or adhesive tape.
   • Place the bar magnet at the center of the paper.
   • Mark the outline of the bar magnet on the paper.
   • Label the north and south poles of the magnet clearly.
2. Tracing Magnetic Field Lines:
   • Place the magnetic compass near one pole of the bar magnet.
   • Mark a dot at the position of the pointer of the compass needle.
   • Move the compass such that the tail of the needle coincides with the previously marked dot.
   • Mark another dot at the position of the pointer.
   • Continue this process until you reach the other pole of the magnet.
   • Join all the dots with a smooth curve to get one magnetic line of force.
   • Repeat the procedure to draw several magnetic lines of force by starting from different positions around one pole.
3. Locating Neutral Points:
   • Place the magnet such that its north pole points towards the geographic north.
   • Move the compass slowly along the axial line on both sides of the magnet.
   • Look for positions where the compass needle becomes unstable or rotates freely.
   • Mark these positions as neutral points.

Field Line Measurements:

Line No.	Starting Position (from N-pole)	Points Marked (coordinates in cm)	Field Direction
1
2
3
4
5

Neutral Points:

Neutral Point	Position (x, y) in cm	Distance from Center of Magnet (cm)
1
2

1. Calculating Field Strength at Different Points:

For any point at a distance $r$ from the center of the magnet, the magnetic field strength can be calculated using:

2. Verifying Inverse Cube Law:

Plot a graph of field strength ($B$) versus distance ($r$). If the law is followed, the graph of $B$ vs $\frac{1}{r^3}$ should be a straight line.

3. Calculating Magnetic Moment:

If the field strength at a known point is measured, the magnetic moment can be calculated by rearranging the formula:

4. Locating Neutral Points:

For a bar magnet placed in the Earth's magnetic field, the neutral points occur where:

Where $B_E$ is the horizontal component of Earth's magnetic field.

This can be rearranged to find the theoretical distance of neutral points:

1. The magnetic lines of force around the bar magnet were successfully traced.
2. The magnetic field lines form closed loops that emerge from the north pole and enter the south pole.
3. The field lines are closer near the poles indicating stronger magnetic field in those regions.
4. The neutral points were located at a distance of approximately _____ cm from the center of the magnet.
5. The pattern of the magnetic field lines demonstrates that the magnetic field follows the inverse cube law.

1. Keep the bar magnet away from other magnetic materials during the experiment.
2. Ensure that the drawing board is horizontal and free from vibrations.
3. The compass needle should be free to rotate without any friction.
4. Mark the outline of the magnet accurately on the paper.
5. When tracing a field line, ensure that the tail of the compass needle exactly coincides with the previously marked dot.
6. Keep electronic devices away from the experimental setup as they may interfere with the magnetic field.
7. Handle the bar magnet carefully to avoid demagnetization due to dropping or heating.
8. Use a small compass to get more accurate results, especially near the poles where the field lines are dense.
9. Take readings at shorter intervals near the poles for better accuracy.
10. Do not move the paper or the magnet once the experiment has started.