An aeroplane in which the distance between the tips of wings is 50 m is flying horizontally with a speed of 360 km/hr over a place where the vertical component of earth magnetic field is $2.0\times {10}^{-4}$ $\mathrm{weber}/{\mathrm{m}}^2$. The potential difference between the tips of wings would be:

A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 ms^-1 at right angle to the horizontal component of the earth's magnetic field, \(0.30 \times 10^{-4} \mathrm{~Wb} \mathrm{~m}^{-2}\)$\mathrm{}$.
The instantaneous value of the emf induced in the wire is:

A magnetic rod is inside a coil of wire which is connected to an ammeter. If the rod is stationary, which of the following statements is true?

A \(1~\text{m}\) long metallic rod is rotating with an angular frequency of \(400~\text{rad/s}\)$$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of \(0.5~\text{T}\) parallel to the axis exists everywhere. The emf induced between the center and the ring is:
1. \(200~\text{V}\)
2. \(100~\text{V}\)
3. \(50~\text{V}\)
4. \(150~\text{V}\)

A square metallic wire loop of side \(0.1\) m and resistance of \(1~\Omega\) is moved with a constant velocity in a magnetic field of \(2~\text{wb/m}^2\) as shown in the figure. The magnetic field is perpendicular to the plane of the loop and the loop is connected to a network of resistances. What should be the velocity of the loop so as to have a steady current of \(1\) mA in the loop?

A wire cd of length \(l\) and mass \(m\) is sliding without friction on conducting rails \(ax\) and \(by\) as shown. The vertical rails are connected to each other with a resistance \(R\) between \(a\) and \(b\). A uniform magnetic field \(B\) is applied perpendicular to the plane \(abcd\) such that \(cd\) moves with a constant velocity of:

A conductor ABOCD moves along its bisector with a velocity of \(1\) m/s through a perpendicular magnetic field of \(1~\text{wb/m}^2\), as shown in fig. If all the four sides are of \(1\) m length each, then the induced emf between points A and D is:
                  
1. \(0\)

2. \(1.41\) volt

3. \(0.71\) volt

4. None of the above

Consider the situation shown in the figure. The wire AB is sliding on the fixed rails with a constant velocity. If the wire AB is replaced by semicircular wire, the magnitude of the induced current will:

A conducting square frame of side \(a\) and a long straight wire carrying current \(i\) are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity \(v\). The emf induced in the frame will be proportional to:
                
1. \(\frac{1}{x^2}\)
2. \(\frac{1}{(2x-a)^2}\)
3. \(\frac{1}{(2x+a)^2}\)
4. \(\frac{1}{(2x-a)\times (2x+a)}\)

When a conducting wire \(XY\) is moved towards the right, a current flows in the anti-clockwise direction. Direction of magnetic field at point \(O\) is: