Physics Test - 2

CONCEPT:

• Principle of superposition: When two or more waves come together at some point in space then the resultant disturbance wave is the vector sum of disturbance of the individual waves.

Interference:

• When two waves superimpose then the resultant amplitude of the wave at that point is the vector sum of amplitudes of each individual wave. This phenomenon is called the interference of waves.
• There are two types of 
  1. Constructive Interference: 
  2. Destructive Interference: 

CALCULATION:

CONCEPT:

Electric dipole in a uniform external field:

• We know that when a charge q is placed in electric field E, it experiences a force F, the force is given as,

⇒ F = qE

• So when an electric dipole is placed in the electric field according to the diagram,

The force on the +q and the -q charge due to the electric field is given as,

⇒ F = qE

• The net force on the electric dipole will be zero.
• The torque on the electric dipole is given as,

⇒ τ = pE.sinθ

Where θ = angle between the dipole and the electric field

• This torque will tend to align the dipole with the electric field.

EXPLANATION:

• The torque on the electric dipole in an external uniform electric field is given as,

Where θ = angle between the dipole and the electric field

• Hence, option 4 is correct.

CONCEPT:

Capacitor:

• The capacitor is a device in which electrical energy can be stored.
  • In a capacitor two conducting plates are connected parallel to each other and carrying charges of equal magnitudes and opposite sign and separated by an insulating medium.
  • The space between the two plates can either be a vacuum or an electric insulator such as glass, paper, air, or semi-conductor called a dielectric.​

​Parallel plate capacitor:

• A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance.
• The space between the two plates can either be a vacuum or an electric insulator such as glass, paper, air, or semi-conductor called a dielectric.​
• The electric field intensity at the outer region of the parallel plate capacitor is always zero whatever be the charge on the plate.
• The electric field intensity in the inner region between the plates of a parallel plate capacitor remains the same at every point.
• The electric field intensity in the inner region between the plates of a parallel plate capacitor is given as,

Where A = area of the plates, d = distance between the plates, Q = charge on the plates, and σ = surface charge density

EXPLANATION:

For a parallel plate capacitor,

When A = area of the plates, d = distance between the plates, and Q = charge on the plates

• The electric field intensity between the plates of the capacitor is given as,

• Hence, option 1 is correct.

Additional Information

If the dielectric medium of dielectric constant K is filled between the plates:

• When the dielectric medium is filled in the space between the plates of the parallel plate capacitor, its capacitance increases.
• The electric field intensity in the inner region between the plates of a parallel plate capacitor is given as,

CONCEPT:

• The property by which an electric conductor opposes the flow of current through it is called as resistance of the conductor.
• It is denoted by R.
• The SI unit of resistance is Ohm (Ω).

Where ρ = resistivity of conductor, l = length of conductor and A = cross-sectional area.

EXPLANATION:

Given that;

• When we stretch the wire then length increases but cross-sectional are decreases. But the total volume of the wire will remain constant. So we will write the formula of resistance in terms of volume (V).

⇒ Volume (V) = area (A) × length (l)

So A = V/l

CONCEPT:

Electric charge(q): The property of matter which is responsible for electrostatic force is called an electric charge.

The SI unit of charge is coulomb (C).

The rate of flow of electric charge is called an electric current.

Charge (q) = current (I) × time (t)

CALCULATION:

Given that;

Current (I) = 10 A

Time (t) = 2 hrs = 2 × 60 × 60 sec

Amount of electric Charge (q) = current (I) × time (t) = 10 × 2 × 60 × 60 = 72000 C

The amount of 72000 Coulomb flows through this circuit. So option 2 is correct.

CONCEPT:

• First Law of Thermodynamics: The conservation of energy principle to heat and thermodynamic processes:
• The change in the internal energy of a system is equal to the heat added to the system minus the work done by the system.

ΔE = Q - W

ΔE = Change in internal energy.

Q = Heat added to the system

W = Work done by the system.

• The first law makes use of the key concepts of internal energy, heat, and system work. It is used extensively in the discussion of heat engines. 

EXPLANATION:

• Internal energy depends only on the initial and final states of temperature and not on the path. 
• In a cyclic process, as initial and final states are the same, change in internal energy is zero (ΔE = 0).
• Hence E is ΔU, the change in internal energy.

​option 1 is correct.

CONCEPT:

Torque on a rectangular current loop in a uniform magnetic field:

• If a rectangular loop carrying a steady current is placed in a uniform magnetic field then it will experience a torque.
  • The net force on the loop will be zero.
• The torque on the current-carrying rectangular loop is given as,

⇒ τ = NIAB.sinθ

Where N = number of turns in the coil, I = current in the loop, A = area enclosed by the loop, B = magnetic field intensity, and θ = angle between the normal to the plane of the coil and the direction of a uniform magnetic field

• The magnetic moment m for the loop is given as,

⇒ m = NIA

So,

EXPLANATION:

For case 1:

τ = torque on the loop, l = length of the loop, b = width of the loop, I = current in the loop, B = uniform magnetic field, and θ = angle between the normal to the plane of the coil and the direction of a uniform magnetic field

• The area enclosed in the loop is given as,

⇒ A = lb      -----(1)

• Then the torque on the current-carrying rectangular loop is given as,

⇒ τ = NIAB sinθ    -----(2)

For case 2:

τ' = torque on the loop, l' = length of the loop, b' = width of the loop, I = current in the loop, B = uniform magnetic field, and θ = angle between the normal to the plane of the coil and the direction of a uniform magnetic field

⇒ l' = 2l

⇒ b' = 2b

• The area enclosed in the loop is given as,

⇒ A' = l'b'

⇒ A' = 2l×2b

⇒ A' = 4lb

⇒ A' = 4A      -----(3)

• Then the torque on the current-carrying rectangular loop is given as,

⇒ τ' = NIA'B.sinθ

⇒ τ' = 4×NIAB.sinθ    -----(4)

By equation 2 and equation 4,

⇒ τ' = 4τ

• Hence, option 3 is correct.

CONCEPT:

Elements of Earth's Magnetic Field:

• The magnitude and direction of the magnetic field of the earth at a place are completely given by certain quantities known as magnetic elements.

Magnetic Declination (θ):

• It is the angle between geographic and magnetic meridian planes. 
• Declination at a place is expressed at θ° E or θ° W depending upon whether the north pole of the compass needle lies to the east or the west of the geographical axis.

The angle of inclination or Dip (Φ):

• It is the angle between the direction of the intensity of the total magnetic field of earth and a horizontal line in the magnetic meridian.

EXPLANATION:

• The magnetic inclination or Angle of dip is one of the techniques used to measure the polarity of the earth’s magnetic field.
• The angle made by the earth’s total magnetic field, B with the horizontal direction in the magnetic meridian is called as the magnetic inclination at that place
• It is the angle by which the total intensity of the earth’s magnetic field dips or comes out of the horizontal plane. It is different at different places and measured using a “Dip Circle”.
• At the magnetic equator, the dip needle rests horizontally at an angle of zero degrees while, at the magnetic poles, the magnetic needle rests vertically, at an angle of 90 degrees.
• At all the other places, the angle of dip is between 0° and 90°.

Concept:  

The movement of energy from one place to another is called energy transfer. Heat transfer mainly takes place due to temperature differences.

There are three modes of Heat transfer.

1.Conduction: The mode of heat transfer in solids where heat transfer takes place without the movement of medium particles is called conduction.

For example:  By heating one end of a metal rod we can feel the heat at the other end.

2.Convection: The mode of heat transfer in fluids where heat transfer takes place due to the movement of particles of the medium is called convection.

For example: Heating of water in a pot

3. Radiation: The mode of heat transfer where heat is transferred from one place to another without affecting the medium particles is called radiation.

For example: When we place our hands near the burning gas stove, then we can feel the heat. This is due to radiation.

Explanation:

From the above explanation, we can see that, there are three modes in which heat energy can be transferred from one point to another and these modes of heat transfer are conduction, convection, and radiation.

And in our case, as a person starts walking, the heat is transferred from the hot surface to a person's feet and hence option 1 is correct among all.

The correct answer is option 2) i.e. A/m²

CONCEPT:

• Current density is defined as the amount of electric charge flowing across a unit cross-sectional area in unit time.
  • It is a vector quantity.

The electric current density (J) for a given conducting material is given as:

Where q is the electric charge flowing, t is the time, I is the current flowing and A is the cross-sectional area.

EXPLANATION:

• The SI units for current and area are A and m² respectively.

Thus, the SI unit of current density is A/m².