Solenoid Experiment : Draw and study Magnetic Lines of Force

Magnetic Lines of Force Due to a Solenoid

1. Aim

To draw and study the magnetic lines of force produced by a current-carrying Solenoid and to verify that the magnetic field inside a solenoid is uniform.

2. Apparatus Used

Solenoid (with multiple turns of insulated copper wire)
Cardboard or acrylic sheet
Battery or DC power supply (6-12V)
Rheostat (variable resistor)
Ammeter (0-5A)
Switch
Connecting wires
Iron filings
Small plotting compasses
White paper sheets
Drawing board and drawing pins

3. Diagram

Fig. 1: Experimental setup for studying magnetic lines of force due to a solenoid

4. Theory

A solenoid is a long coil of wire wound in the form of a helix. When an electric current passes through it, a magnetic field is generated around it. The magnetic field pattern of a solenoid resembles that of a bar magnet. One end of the solenoid behaves as a north pole and the other end as a south pole.

The magnetic field due to a solenoid can be understood using Ampere's circuital law, which relates the integrated magnetic field around a closed loop to the electric current passing through the loop.

Inside a solenoid, the magnetic field is approximately uniform and parallel to the axis of the solenoid. Outside the solenoid, the magnetic field is similar to that of a bar magnet, with the field lines emerging from the north pole and entering the south pole.

The direction of the magnetic field can be determined using the right-hand grip rule: When the fingers of the right hand are curled in the direction of the current in the windings, the thumb points in the direction of the magnetic field inside the solenoid.

The strength of the magnetic field inside a solenoid depends on:

The current flowing through the solenoid
The number of turns per unit length (turn density)
The type of core material (air core, iron core, etc.)

5. Formula

The magnetic field $B$ inside a long solenoid with an air core is given by:

$$B = \mu_0 n I$$

Where:

$B$ = Magnetic field strength inside the solenoid (in tesla, T)
$\mu_0$ = Permeability of free space = $4\pi \times 10^{-7} \, \text{H/m}$
$n$ = Number of turns per unit length = $\frac{N}{L}$ (in turns/meter)
$N$ = Total number of turns in the solenoid
$L$ = Length of the solenoid (in meters)
$I$ = Current flowing through the solenoid (in amperes)

For a solenoid with a ferromagnetic core, the formula becomes:

$$B = \mu_0 \mu_r n I$$

Where $\mu_r$ is the relative permeability of the core material.

6. Procedure

Set up the apparatus as shown in the diagram, connecting the solenoid, switch, rheostat, ammeter, and power supply in series.
Place the solenoid horizontally on the drawing board.
Fix a sheet of white paper on the drawing board using drawing pins.
Place the solenoid over the paper and mark its position by drawing its outline.
Mark the direction of current flow through the solenoid.
Identify and mark the north and south poles of the solenoid using the right-hand grip rule or a compass.
Place a small plotting compass at a point near one end of the solenoid.
Close the switch to allow current to flow through the solenoid.
Note the direction in which the compass needle points. This indicates the direction of the magnetic field at that point.
Mark the position of the compass needle by making two dots at the ends of the needle.
Move the compass slightly in the direction of the north pole of the needle.
Again note the direction of the compass needle and mark its position.
Repeat steps 11 and 12 until a complete field line is traced from one end of the solenoid to the other.
Trace more field lines by starting from different positions around the solenoid.
Alternatively, sprinkle iron filings uniformly over the paper and gently tap the board. The iron filings will align along the magnetic field lines.
For studying the field inside the solenoid, use a specially designed apparatus with a solenoid mounted on a cardboard or acrylic sheet, allowing you to place compasses inside the coil.
Once the field lines are established, draw them properly with arrows indicating the direction of the field.
Turn off the power supply and disconnect the circuit.

7. Observation Table

For measurements of magnetic field strength at different positions:

S.No.	Current through solenoid (A)	Position along the axis (cm)	Position from the center (cm)	Compass deflection angle (degrees)	Observations about field line pattern
1
2
3
4
5

For verification of uniformity of the magnetic field inside the solenoid:

S.No.	Current (A)	Position inside the solenoid (cm from left end)	Direction of compass needle	Is the field parallel to the axis? (Yes/No)
1
2
3
4
5

8. Calculations

1. Calculate the magnetic field strength inside the solenoid using the formula:

$$B = \mu_0 n I$$

Example calculation:

Given:
Number of turns in the solenoid (N) = [Value]
Length of the solenoid (L) = [Value] m
Current flowing through the solenoid (I) = [Value] A

Turn density:

$$n = \frac{N}{L} = \frac{[\text{Value}]}{[\text{Value}]} = [\text{Value}] \text{ turns/m}$$

Magnetic field strength:

\begin{align} B &= \mu_0 n I \\ &= 4\pi \times 10^{-7} \times [\text{Value}] \times [\text{Value}] \\ &= [\text{Value}] \text{ tesla (T)} \end{align}

2. Compare the theoretical value with your observations based on the pattern of magnetic field lines.

9. Result

The magnetic field lines around a solenoid were successfully traced and drawn.
Observations confirmed that the magnetic field lines inside the solenoid are approximately parallel to the axis and uniform in strength, as predicted by theory.
The magnetic field outside the solenoid was observed to resemble that of a bar magnet, with field lines emerging from one end (north pole) and entering the other end (south pole).
The direction of the magnetic field was found to follow the right-hand grip rule.
The calculated theoretical value of the magnetic field inside the solenoid is [Value] tesla, which is [in agreement/shows a deviation of x%] with our observations.

10. Precautions

Ensure that all connections are tight and secure.
Use a rheostat to control the current to prevent overheating of the solenoid.
Do not keep the circuit connected for a long time to avoid heating of the solenoid.
Keep magnetic materials away from the experimental setup to avoid interference with the magnetic field.
The compass needle used should be small and sensitive.
The compass should be moved carefully without disturbing the paper.
Ensure that the solenoid is properly positioned on the paper.
When using iron filings, sprinkle them gently and uniformly.
Tap the board gently to allow the iron filings to align properly along the field lines.
Ensure that the plotting compass is not magnetized permanently due to the strong field of the solenoid.
The solenoid should be sufficiently long to approximate an ideal solenoid with uniform field inside.

11. Viva Voice Questions

Q1: What is a solenoid?

A solenoid is a long coil of wire wound in the form of a helix. When an electric current passes through it, it creates a magnetic field similar to that of a bar magnet, with one end acting as a north pole and the other as a south pole.

Q2: How can you determine the polarity of a solenoid?

The polarity of a solenoid can be determined using the right-hand grip rule: when you curl the fingers of your right hand in the direction of the current flow in the coil, your thumb points toward the north pole of the solenoid.

Q3: What is the shape of the magnetic field inside a solenoid?

Inside a solenoid, the magnetic field lines are approximately parallel to the axis of the solenoid and uniform in strength, especially in the central region away from the ends.

Q4: Why is the magnetic field inside a solenoid stronger than outside?

Inside the solenoid, the magnetic fields due to individual turns add up constructively to create a strong, uniform field. Outside the solenoid, the magnetic fields from different parts of the solenoid tend to partially cancel each other, resulting in a weaker field.

Q5: How does the magnetic field of a solenoid depend on current?

The magnetic field strength inside a solenoid is directly proportional to the current flowing through it. If the current doubles, the magnetic field strength also doubles.

Q6: What would happen to the magnetic field if an iron core is inserted into the solenoid?

Inserting an iron core into the solenoid would significantly increase the magnetic field strength due to the high relative permeability of iron. The iron core becomes magnetized and adds to the original field, resulting in a stronger electromagnet.

Q7: Compare the magnetic field pattern of a solenoid with that of a bar magnet.

The magnetic field pattern of a solenoid is similar to that of a bar magnet. Both have field lines emerging from the north pole and entering the south pole, forming closed loops. However, the field inside a solenoid is more uniform than inside a bar magnet.

Q8: Why do we use a rheostat in the circuit?

A rheostat is used to control the current flowing through the solenoid. By adjusting the resistance, we can vary the current and hence the strength of the magnetic field, which helps in studying the field pattern at different field strengths.

Q9: What is Ampere's circuital law, and how does it apply to a solenoid?

Ampere's circuital law states that the line integral of the magnetic field around a closed loop is equal to μ₀ times the current enclosed by the loop. For a solenoid, this law can be used to derive the formula for the magnetic field inside the solenoid as B = μ₀nI.

Q10: How would the field pattern change if the current direction is reversed?

If the current direction is reversed, the direction of the magnetic field would also reverse. The north and south poles of the solenoid would interchange, and the direction of the field lines would be reversed.

For More experiment Manual Click on Link...