Question

When a train travels with a speed \(360 \mathrm{~km} \mathrm{~h}^{-1}\) along the track separated by 1 meter. The vertical component of earth's magnetic field is \(0.1 \times 10^{-4} \mathrm{~T}\). What is the value of induced emf between the rails? (a) \(10^{-2} \mathrm{~V}\) (b) \(10^{-4} \mathrm{~V}\) (c) \(10^{-3} \mathrm{~V}\) (d) \(1 \mathrm{~V}\)

Short answer

The short answer is: (a) $10^{-2} \mathrm{~V}$

Step-by-step solution

To convert the velocity from km/h to m/s, multiply it by (1000 m/km) / (3600 s/h). \(v = 360 \frac{km}{h} \times \frac{1000m}{1km} \times \frac{1h}{3600s} \) #Step 2: Substitute values into the EMF formula#

Plug the values for B, v, and L into the EMF formula: EMF = B * v * L where B = 0.1 × 10^{-4} T, v = (calculated in step 1) and L = 1 m. #Step 3: Calculate induced EMF between the rails#

Now, calculate the induced EMF by multiplying the values as follows: EMF = (0.1 × 10^{-4} T) * (value obtained in step 1) * (1 m) #Step 4: Compare result with given options and select the correct one#

After calculating the EMF, compare the result with the given options (a) to (d) and select the one that matches the value you found.

Key concepts

Induced EMF

Induced electromotive force (EMF) is a concept that describes how voltage is generated in a conductor when it moves through a magnetic field. You can think of it as a by-product of a conductor's interaction with a magnetic field, which forces the electrons in the conductor to move, creating a voltage. The process is quantitative, meaning we can calculate the induced EMF using the formula: \( \text{EMF} = B \times v \times L \). Here:

• B represents the magnetic field strength.
• v is the velocity of the conductor through the field.
• L is the length of the conductor perpendicular to the magnetic field.

To calculate the induced EMF between the rails, consider how the direction and speed of the train, the magnetic field's strength, and the distance between the rails influence each other. These factors work together to generate a potential difference across the rails, which is the induced EMF.

Magnetic Field

A magnetic field is an invisible force that exerts influence on charged particles and magnetic materials. The Earth's magnetic field, for example, is what makes compass needles point north. It's also crucial to understanding electromagnetic concepts because it can induce electricity in conductors moving through it.

In this scenario, the vertical component of the Earth's magnetic field is given as \(0.1 \times 10^{-4} \mathrm{~T}\). This component is important for calculating the induced EMF, as it represents the part of the magnetic field that directly contributes to the generation of voltage when the conductor moves vertically relative to the field. Without this aspect of the magnetic field, the entire process of electromagnetic induction would not occur.

Electromagnetic Induction

Electromagnetic induction is a fundamental concept in physics that explains how a change in magnetic environment of a coil of wire will produce voltage across the coil. The same concept underlies many electrical technologies and is a cornerstone of understanding how electric generators and transformers work. When a conductor moves through a magnetic field, the magnetic lines of force cut across the conductor, and this motion sets up a current in a circuit if it forms a closed loop.

The principle of electromagnetic induction, formulated by Faraday, is expressed in Faraday's law of induction, which quantifies the induced EMF as equal to the rate of change of the magnetic flux through the loop. In the case of our rail track system, the train moving through Earth's magnetic field changes the magnetic flux, thereby inducing an EMF between the rails.

Rail Track System

The rail track system offers a practical example of electromagnetic induction in action. As a train travels along the tracks, it acts as a moving conductor cutting through the Earth’s magnetic field. This cuts the magnetic flux lines, inducing an EMF due to motion through a magnetic field.

A few key points considered are:

• The uniform track spacing which acts as the length parameter 'L' in the EMF formula.
• The speed of the train that serves as the velocity 'v'.
• The Earth's magnetic field's perpendicular component considered as the magnetic field 'B'.

This system effectively showcases how mechanical motion converts into electrical signals via electromagnetic principles. By understanding this setup, students can visualize the physical process leading to EMF creation and appreciate the practical applications of magnetic induction.