Question

The two rails of a railway track, insulated from each other and the ground, are connected to millivoltmeter. What is the reading of the millivoltmeter when a train passes at a speed of $180 \mathrm{km} / \mathrm{hr}$ along the track, given that the vertical component of earth's magnetic field is $0.2 \times 10^{-4} w b / m^{2}$ and rails are separated by 1 metre.
A. ${{10}^{-1}}\text{volt }$
B. 10 mV
C. 1 volt
D. 1 mV

Answer 1

We know that a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), that is to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F. Force is the push or pull applied on an object. It can move a stationary object or stop a moving object. Force can also change the speed and direction of a moving object. When force is applied on an object, resulting in the movement of that object, work is said to be done. Based on this concept we have to solve this question.

Complete step by step answer
We can see that here, Speed of the train, $\mathrm{v}=\dfrac{180 \times 1000}{3600}=50 \mathrm{m} \mathrm{s}^{-1}$
Vertical component of earth's magnetic field, $\mathrm{B}_{\mathrm{v}}=0.2 \times 10^{-4} \mathrm{T}$.
Separation between the rails, $1=1 \mathrm{m}$
The induced emf generated is given by
$\varepsilon =-\dfrac{\text{d}\phi }{\text{dt}}$
$=-\dfrac{\text{d}}{\text{dt}}(\text{BA})$
$=-\text{B}\dfrac{\text{dA}}{\text{dt}}$
where, $\mathrm{A}$ is the area and $\mathrm{B}$ is the magnetic field.
If I is denoted as the distance between the rails and $v$ is the speed of the train, then
Induced EMF, e$=-\text{B}\mid \text{v}|\text{e}|$
$=0.2\times {{10}^{-4}}\times 1\times 50$
$=1\times {{10}^{-3}}\text{V}=1\text{mV}$
Hence, the millivoltmeter will read $1 \mathrm{mV}$.

Therefore, the correct answer is Option D.

Note: We should know that if an object's speed or velocity is increasing at a constant rate then we say it has uniform acceleration. The rate of acceleration is constant. If a car speeds up then slows down then speeds up it doesn't have uniform acceleration. The instantaneous acceleration, or simply acceleration, is defined as the limit of the average acceleration when the interval of time considered approaches 0. It is also defined in a similar manner as the derivative of velocity with respect to time. If an object begins acceleration from rest or a standstill, its initial time is 0. If we get a negative value for acceleration, it means the object is slowing down. The acceleration of an object is its change in velocity over an increment of time. This can mean a change in the object's speed or direction. Average acceleration is the change of velocity over a period of time. Constant or uniform acceleration is when the velocity changes the same amount in every equal time period.