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.