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Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

If we rotate the dipole of moment $p$ placed in an electric field $E$ from an $\theta _1$ to $\theta _2$, the work done by the external force is

  1. $pE(\cos \theta _2 - \cos \theta _1)$
  2. $pE(\cos \theta _1 - \cos \theta _2)$
  3. $pE(\sin \theta _2 - \sin \theta _1)$
  4. $pE(\sin \theta _1 - \sin \theta _2)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given dipole of dipole moment $p$ in an electric field $E$. It is rotated from $\theta _{1}$ to $\theta _{2}$. We have to find the work done by external force.
When a dipole of dipole moment  $p$ is placed in electric field, work done in rotated the dipole by angle $\theta$ is
$W=-pE \cos{\theta _{1}}$
Now work done in rotating dipole by $\theta _{1}$ is 
$W _{2}=-pE\cos{\theta _{2}}$
Work done in rotating the dipole from $\theta _{1}$ to $\theta _{2}$ is
$W=W _{2}-W _{1}$
$=-pE \cos{\theta _{2}}-(-pE \cos{\theta _{1}})$
$=pE(\cos{\theta _{1}}-\cos{\theta _{2}})$
Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

An electric dipole of dipole moment $p$ is placed in a uniform electric field $E$ in stable equilibrium position. Its moment of inertia about the centroidal axis is $I$. If it is displaced slightly from its mean position find the period of small oscillations.

  1. $2\pi \sqrt{\dfrac{I}{2pE}}$
  2. $2\pi \sqrt{\dfrac{2I}{pE}}$
  3. $2\pi \sqrt{\dfrac{I}{pE}}$
  4. $\pi \sqrt{\dfrac{2I}{pE}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Dipole moment $=p$
electric field $=E$
centroid axis $=I$
Explanation
When displaced at an angle $\theta $ from its mean position the magnitude of restoring torque is $T=-psin\theta $
For small angular displacement $\sin\theta \approx \theta $
$T=-pE\theta $
$\alpha =\dfrac { T }{ I } =-\left( \dfrac { PE }{ I }  \right) \theta $
    $={ -w }^{ 2 }\theta $
${ w }^{ 2 }=\dfrac { PE }{ I } $
$T=2\pi \sqrt { \dfrac { I }{ PE }  } $
($P.E=$ moment in electric field)
Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however not constant but increases uniformly along the positive z-direction at the rate ${10^5}\,V/m.$ The force and the torque experienced by a system having a total dipole moment equal to ${10^{ - 7}}C - m$ in the negative z-direction is given by respectively.

  1. 0.01,0

  2. 0.02,0

  3. 0,0.01

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$z$ direction positive rate $={ 10 }^{ 5 }V/m$

torque $=$ M $\times$ $E$
            $={ 10 }^{ 5 }\times { 10 }^{ -7 }$
            $=0.01cm$

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

 An electric dipole consist of two opposite charges each of magnitude $1\mu C$ separated by a distance of $2\,cm.$ The dipole is placed in an external field of ${10^5}{\text{N/C}}$.The maximum torque on the dipole is:

  1. $2 \times {10^{ - 4}}J$
  2. $2 \times {10^{ - 3}}J$
  3. $4 \times {10^{ - 3}}J$
  4. ${10^{ - 3}}N\,m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
An electric dipole consist at two opposite charge each of magnitude $=1\mu C=1\times { 10 }^{ -6 }C$
distance $=2cm$
Exter field $={ 10 }^{ 5 }N/C$
maximum torque on the dipole $=?$
$q=1\times { 10 }^{ -6 }C,\quad 2a=2cm$
                                or,  $=0.02cm$
$\therefore$    $P=q\times 2a$
           $=\left( 1\times { 10 }^{ -6 } \right) \times 0.02$
           $=2\times { 10 }^{ -8 }cm$
Intensity of the external electric field, $E=1.0\times { 10 }^{ 5 }N/C$
(i) ${ Z } _{ max }=pE=\left( 2\times { 10 }^{ -8 } \right) \left( 10\times { 10 }^{ 5 } \right) =2\times { 10 }^{ -3 }N-m$
(ii) Net work done in turning the dipole from ${ 0 }^{ 0 }$ to ${ 180 }^{ 0 }$
i.e  $W=\int _{ { 0 }^{ 0 } }^{ { 180 }^{ 0 } }{ \overline { r }  } d\theta =\int _{ { 0 }^{ 0 } }^{ { 180 }^{ 0 } }{ pE\sin\theta  } d\theta $
           $=pE{ \left[ -cos\theta  \right]  } _{ { 0 }^{ 0 } }^{ { 180 }^{ 0 } }$
           $=-pE\left( { \cos180 }^{ 0 }-\cos{ 0 }^{ 0 } \right) $
           $=2pE$
           $=2\times \left( 2\times { 10 }^{ -8 } \right) \left( 1\times { 10 }^{ 5 } \right) J$
           $=4\times { 10 }^{ -3 }J$
Multiple choice physics electric charges and fields conductors and insulators introduction to electrostatics electricity

State whether true or false.
Metals as compared to non-metals are generally bad conductors of electricity.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Metals are good conductors of electricity while non metals are bad conductivity as metal has lot of free electrons and therefore conducts while non metal  does not have any free electron and does not conduct electricity.So the answer is false.

Multiple choice physics electric charges and fields conductors and insulators introduction to electrostatics electricity

State whether true or false.
A jute string can be used to make a circuit instead of metal wires,

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A jute string cannot be used to make a circuit as jute is an insulator and does not conduct electricity while metal is a conductor of electricity, hence, metal wires can be used to make a circuit.

Hence, given statement is false.

Multiple choice physics electric charges and fields conductors and insulators introduction to electrostatics electricity

Glass wool is a . . . . conductor of electricity.

  1. good

  2. bad

  3. very good

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Glass wool is an insulating material made from fibres of glass arranged using a binder into a texture similar to wool. The process traps many small pockets of air between the glass, and these small air pockets result in the thermal insulation properties.
Glass wool is produced in rolls or in slabs, with different thermal and mechanical properties. It may also be produced as a material that can be sprayed or applied in place, on the surface to be insulated.
They possess very low expansion property, remarkable thermal shock resistance, low thermal conductivity, excellent electrical insulation up to 1000 C, and excellent resistance to corrosion from molten metal. 
Hence, Glass wool is a poor conductor of electricity.

Multiple choice physics electric charges and fields conductors and insulators introduction to electrostatics electricity

Aluminium metal is :

  1. magnetic substance

  2. bad conductor of heat

  3. good conductor of electricity

  4. bad conductor of electricity
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The electrical conductivity of matter is dependent upon the atomic structure of the material from which the conductor is made. In any solid material, such as copper, the atoms which make up the molecular structure are bound firmly together. At room temperature, copper will contain a considerable amount of heat energy. Since heat energy is one method of removing electrons from their orbits, copper will contain many free electrons that can move from atom to atom. When not under the influence of an external force, these electrons move in a zigzag manner within the conductor. This movement is equal in all directions so that electrons are not lost or gained by any part of the conductor. When controlled by an external force, the electrons move generally in the same direction. The effect of this movement is felt almost instantly from one end of the conductor to the other. This electron movement is called an ELECTRIC CURRENT.
Some metals are better conductors of electricity than others. Silver, copper, gold, and aluminum are materials with many free electrons and make good conductors. Silver is the best conductor, followed by copper, gold, and aluminum. Copper is used more often than silver because of cost. Aluminum is used where weight is a major consideration, such as in high-tension power lines, with long spans between supports. Gold is used where oxidation or corrosion is a consideration and a good conductivity is required.
Hence, Aluminium is a good conductor of electricity.

Multiple choice physics electric charges and fields conductors and insulators introduction to electrostatics electricity

Mica is a ____ conductor of electricity.

  1. good

  2. bad

  3. positive

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The electrical and thermal conduction properties of a material can be similar or very different, in metals the electrical and thermal conductivity is due to free electrons, in non-metals thermal conductivity has nothing to do with free electrons, but more to do with lattice vibrations (that is, phonons). 
So mica has good thermal conductivity due to phonons, but doesn't have sufficient free electrons and a very high resistance to be a good conductor of electricity.
Hence, Mica is a poor or bad conductor of electricity.