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At what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524.
Net electric flux through a cube is the sum of fluxes through its six faces. Consider a cube as shown in figure, having sides of length L = 10.0cm. The electric field is uniform, has a magnitude E = 4.00 × 103N C-1 and is parallel to the xy plane at an angle of 37º measured from the + x - axis towards the + y - axis.

  1. Electric flux passing through surface S6 is:
  1. -24N mC-1
  2. 24N mC-1
  3. 32N mC-1
  4. -32N mC-1
  1. Electric flux passing through surface S1 is:
  1. -24N mC-1
  2. 24N m2 C-1
  3. 32N m2 C-1
  4. -32N m2 C-1
  1. The surfaces that have zero flux are:
  1. S1 and S3
  2. S5 and S6
  3. S2 and S4
  4. S1 and S2
  1. The total net electric flux through all faces of the cube is:
  1. 8N m2 C-1
  2. -8N m2 C-1
  3. 24N m2 C-1
  4. Zero.
  1. The dimensional formula of surface integral $\oint\vec{\text{E}}\cdot\text{d}\vec{\text{S}}$ of an electric field is:
  1. [M LT-2 A-1]
  2. [M LT-3 A-1]
  3. [M L-1 T3 A-3]
  4. [M L-3 T-3 A-1]
A lady cannot see objects closer than 40cm from the left eye and closer than 100cm from the right eye. While on a mountaineering trip, she is lost from her team. She tries to make an astronomical telscope from her reading glasses to look for her teammates.
  1. Which glass should she use as the eyepiece?
  2. What magnification can she get with relaxed eye?
The charge enclosed by a spherical Gaussian surface is $8.85 \times 10^{-8}$ Coulomb. Calculate (a) the electric flux emerging out of the Gaussian surface, (b) what will be the change in electric flux if the radius of the Gaussian surface is doubled?
Shows a rod PQ of length 20.0cm and mass 200g suspended through a fixed point O by two threads of lengths 20.0cm each. A magnetic field of strength 0.500T exists in the vicinity of the wire PQ, as shown in the figure. The wires connecting PQ with the battery are loose and exert no force on PQ.
  1. Find the tension in the threads when the switch S is open.
  2. A current of 2.0A is established when the switch S is closed. Find the tension in the threads now.

The distance between the centres of two insulated charged copper spheres ' $A$ ' and ' $B$ ' which are identical in size is 50 cm and the charge on each is $6.5 \times 10^{-7} C$. A third uncharged sphere ' C ' of the same size was first brought in contact with the sphere ' $A$ ', and then brought in contact with the second sphere ' $B$ ' and finally separated from both. Then find the magnitude of repulsive foce between ' $A$ ' and ' $B$ '.
The magnetic field due to the earth has a horizontal component of $26\mu\text{T}$ at a place where the dip is 60°. Find the vertical component and the magnitude of the field.
The simplest and the most widely used capacitor is the parallel plate capacitor. It consists of two large plane parallel conducting plates, separated by a small distance.

In the outer regions above the upper plate and below the lower plate, the electric fields due to the two charged plates cancel out. The net field is zero.

In the inner region between the two capacitor plates, the electric fields due to the two charged plates add up. The net field is $\frac{\sigma}{\in_0}.$

For a uniform electric field, potential difference between the plates = Electric field x distance between the plates. Capacitance of the parallel plate capacitor is the charge required to supplied to either of the conductors of the capacitor so as to increase the potential difference between then by unit amount.

  1. A parallel plate capacitor is charged and then isolated. The effect of increasing the plate separation on charge, potential and capacitance respectively are:
  1. Increases, decreases, decreases.
  2. Constant, increases, decreases.
  3. Constant, decreases, decreases.
  4. Constant, decreases, increases.
  1. In a parallel plate capacitor, the capacity increases if:
  1. Area of the plate is decreases.
  2. Distance between the plates increases.
  3. Area of the plate is increases.
  4. Dielectric constant decreases.
  1. A parallel plate capacitor has two square plates with equal and opposite charges. The surface charge densities on the plates are $+\sigma$ and $-\sigma$ respectively. In the region between the plates the magnitude of the electric field is:
  1. $\frac{\sigma}{2\in_0}$

  2. $\frac{\sigma}{\in_0}$

  3. 0
  4. None of these.
  1. If a parallel plate air capacitor consists of two circular plates of diameter 8cm. At what distance should the plates be held so as to have the same capacitance as that of sphere of diameter 20cm?
  1. 9mm
  2. 4mm
  3. 8mm
  4. 2mm
  1. If a charge of + 2.0 × 10-8C is placed on the positive plate and a charge of - 1.0 × 10-8C on the negative plate of a parallel plate capacitor of capacitance $1.2\times10^{-3}\mu\text{F},$ then the potential difference developed between the plates is:
  1. 6.25V
  2. 3.0V
  3. 12.5V
  4. 25V
In a microwave oven, the food is kept in a plastic container and the microwave is directed towards the food. The food is cooked without melting or igniting the plastic container. Explain.

'Tile earth's magnetic field at a point on its surface is usually characterised by three quantities: (a) declination (bl inclination or dip and (cl horizontal component of the field. These are known as the elements of the earth's magnetic field. At a place, angle between geographic meridian and magnetic meridian is defined as magnetic declination, whereas angle made by the earth's magnetic field with the horizontal in magnetic meridian is known as magnetic dip.

  1. In a certain place, the horizontal component of magnetic field is $\frac{1}{\sqrt{3}}$ times the vertical component. 'Tile angle of dip at this place is:
  1. $\text{Zero}$

  2. $\frac{\pi}{3}$

  3. $\frac{\pi}{2}$

  4. $\frac{\pi}{6}$

  1. The angle between the true geographic north and the north shown by a compass needle is called as:
  1. Inclination.
  2. Magnetic declination.
  3. Angle of meridian.
  4. Magnetic pole.
  1. Tile angles of dip at the poles and the equator respectively are
  1. 30º, 30º
  2. 0º, 90º
  3. 45º, 90º
  4. 90º, 0º 
  1. A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It
  1. Will become rigid showing no movement.
  2. Will stay in any position.
  3. Will stay in north-south direction only.
  4. Will stay in east-west direction only. 
  1. Select the correct statement from the following.
  1. The magnetic dip is zero at the centre of the earth.
  2. Magnetic dip decreases as we move away from the equator towards the magnetic pole.
  3. Magnetic dip increases as we move away from the equator towards the magnetic pole.
  4. Magnetic dip does not vary from place to place.