Problem 1989 - JEE Physics

Question

The coercively of a bar magnet is \(100 \mathrm{~A} / \mathrm{m}\). It is to be diamagnetism by placing it inside a solenoid of length \(100 \mathrm{~cm}\) and number of turns 50 . The current flowing through the solenoid will be (a) \(4 \mathrm{~A}\) (b) \(2 \mathrm{~A}\) (c) \(1 \mathrm{~A}\) (d) Zero

Step-by-Step Solution

Answer

The current flowing through the solenoid for diamagnetism is \(2 \mathrm{~A}\), which corresponds to option (b).

Step 1: Write down the given values

The given values are: Coercivity of the bar magnet \(H_{c} = 100 \mathrm{~A}\) \(/\) \(\mathrm{m}\), Length of the solenoid \(l = 100 \mathrm{~cm}\) \(= 1 \mathrm{~meter}\) (converting to meters), Number of turns of the solenoid \(N = 50\).

Step 2: Use the coercive field formula

The coercive field formula is \(H_{c} = NI / l\). We can solve this formula for the current \(I\): \(I = \frac{H_{c} \cdot l}{N}\)

Step 3: Substitute the given values in the formula

Now insert the given values into the formula to find the current \(I\): \(I = \frac{(100 \mathrm{~A} / \mathrm{m}) \cdot (1 \mathrm{~m})}{50}\)

Step 4: Calculate the current

Simplify the expression to get the current \(I\): \(I = \frac{100 \mathrm{~A}}{50} = 2 \mathrm{~A}\) The current flowing through the solenoid for diamagnetism is \(2 \mathrm{~A}\), which corresponds to option (b).

Key Concepts

Magnetic Fields

In physics, a magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. It is an essential concept in the study of physics and electromagnetism. A magnetic field is created by electric currents, such as those in wires or in the Earth's core, and by the intrinsic magnetic properties of some materials, such as iron.

The strength and direction of a magnetic field at a point can be described using vector lines that indicate the field's influence in space. These lines form closed loops around current-carrying wires and magnets. The density of these lines shows the strength of the field; closer lines imply a stronger field. In our example of a solenoid, the magnetic field inside can become particularly strong, as the effects of the individual loops of wire may add together.

• The magnetic field (B) inside a long solenoid can be uniform and is determined primarily by the current and the number of turns per unit length.
• The formula for the magnetic field inside a solenoid is given by: \( B = \mu_0 \cdot \frac{N}{l} \cdot I \), where \( \mu_0 \) is the magnetic constant, \( N \) is the number of turns, \( l \) is the length, and \( I \) is the current.

Electromagnetism

Electromagnetism is the branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. It is one of the four fundamental forces of nature and encompasses phenomena like magnetic fields and electric fields.

The interplay between electricity and magnetism was first discovered in the 19th century, leading to advancements in technology and furthering our understanding of physics. Electromagnetic fields are fluctuating fields of all charged particles, and these fields influence the behavior of all objects in the universe. When current passes through a wire, it creates a magnetic field around the wire, and this principle is the foundation of electromagnets used in solenoids.

• In a solenoid, which is essentially a coil of wire, when an electric current flows, an electromagnetic field is generated. This field can be focused and intensified by arranging the wire in a series of loops (coils).
• This amplified field can be used in various applications, ranging from industrial machinery to magnetic resonance imaging (MRI) devices.

Magnet Coercivity

Magnet coercivity is a measure of the resistance of a magnetic material to changes in its magnetization. It is an essential property in characterizing the hardness of magnetized materials. Coercivity is often considered while demagnetizing a magnet or when attempting to magnetize it with another magnetic field.

Coercivity is expressed in terms of magnetic field strength, measured in ampere per meter (A/m). A high coercivity indicates that a magnet retains its magnetization well, while a low coercivity means it can be easily demagnetized.

• The coercivity of a bar magnet in our given exercise is \( 100 \text{ A/m} \), indicating that any external magnetic field or current of equal strength may neutralize the magnetization.
• In the context of a solenoid, achieving magnetic neutrality of the bar magnet involves passing a calculated current to match this coercivity, thereby countering its magnetic field.

Understanding coercivity helps in knowing the energy required to demagnetize a magnet completely. It is a crucial parameter for the design and application of magnetic materials.