CBSE Delhi-Set-2-2012

On the equator,  and therefore the vertical component of earth's magnetic field is also zero.

Microwaves and UV radiations are a part of the electromagnetic spectrum. The physical quantity that remains same for both the radiations is their speed of propagation in vacuum, which is equal to  .

A biconvex lens will act as a plane sheet of glass if it is immersed in a liquid that has the same refractive index as the material of the biconvex lens. In this case, the focal length of the lens becomes infinite.

When an electric field is applied across a conductor, the electrons drift from lower to higher potential. The drift velocity of the electrons gets superimposed on the thermal velocity and as a result, each electron moves in the direction of the resultant of the drift and the thermal velocity. Thus, the resultant velocity and hence the direction of motion may be different for different electrons. The electrons may also collide with ions and may change its direction of motion.

According to the de Broglie hypothesis, a moving material particle (whether big or small) having a momentum ‘p’ will always have a wavelength  associated with it. Such waves are called matter waves or de Broglie waves having a wavelength,

As the temperature of a semi conductor is increased, the number density of electrons and that of holes increases. Therefore, its resistivity decreases with increasing temperature. The following curve shows the variation of resistivity with temperature for a typical semiconductor:

Let us prove this by contradiction.
Let the electric field at a point on the surface of the conductor be in a general direction, at an angle to the surface. The field can be resolved into a perpendicular component and a component parallel to the surface. If the electric field has a non-vanishing component along the surface, the free charges present on the surface would start moving under its influence. This is contrary to the situation since in the static situation, charges are not in motion. Therefore, the electrostatic field does not have a tangential component and must be normal to the surface at all points.

According to the Lenz’s law, the induced current produced in the loop must oppose the cause of increase of magnetic flux when it moves towards the current carrying conductor with a constant speed v. Thus, the current induced in the loop will be in the clockwise direction.

Therefore, the electric field  shows an inverse square relationship whereas, the electric potential ‘V’ shows an inverse relationship with distance ‘r’ as shown below:

Mutual induction is the property by virtue of which, an emf is induced in one coil due to the current changing in the neighboring coil. 
The coefficient of mutual inductance of the two coils is numerically equal to the amount of magnetic flux  linked with the coil when a unit current (I) flows through the other coil and is given by,