Tag: electric charges and fields

Questions Related to electric charges and fields

Four equal positive charges each of magnitude $q$ are placed at the respective vertices of a square of side length $l$. A point charge $Q$ is placed at the centre of the square. Then

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

  1. $Q$ must not be in equilibrium

  2. $Q$ must be in stable equilibrium

  3. $Q$ must be in neutral equilibrium

  4. $Q$ must be in unstable equilibrium

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Correct Option: B

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

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

  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. $pE(\sin \theta _1 - \sin \theta _2)$

Show answer
Correct Option: B
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
$W=W _{2}-W _{1}$
$=-pE \cos{\theta _{2}}-(-pE \cos{\theta _{1}})$
$=pE(\cos{\theta _{1}}-\cos{\theta _{2}})$

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.

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

  1. $2\pi \sqrt{\dfrac{I}{2pE}}$

  2. $2\pi \sqrt{\dfrac{2I}{pE}}$

  3. $2\pi \sqrt{\dfrac{I}{pE}}$

  4. $\pi \sqrt{\dfrac{2I}{pE}}$

Show answer
Correct Option: C
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)

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.

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

  1. 0.01,0

  2. 0.02,0

  3. 0,0.01

  4. None of the above

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Correct Option: A
Explanation:

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

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

 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:

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

  1. $2 \times {10^{ - 4}}J$

  2. $2 \times {10^{ - 3}}J$

  3. $4 \times {10^{ - 3}}J$

  4. ${10^{ - 3}}N\,m$

Show answer
Correct Option: C
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) $
           $=2pE$
           $=2\times \left( 2\times { 10 }^{ -8 } \right) \left( 1\times { 10 }^{ 5 } \right) J$
           $=4\times { 10 }^{ -3 }J$

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

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

  1. True

  2. False

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Correct Option: B
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.

Identify the conductors from the following: 


Eraser, paper, matchstick, copper wire, polythene.

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

  1. eraser

  2. copper wire

  3. paper

  4. polythene

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Correct Option: B
Explanation:

Out of eraser, paper, copper wire, and polythene, only copper wire is the conductor which is used in the conduction and are used in many practical application circuit.

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

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

  1. True

  2. False

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Correct Option: B
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.

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

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

  1. good

  2. bad

  3. very good

  4. None of the above

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Correct Option: B
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.

Aluminium metal is :

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

  1. magnetic substance

  2. bad conductor of heat

  3. good conductor of electricity

  4. bad conductor of electricity

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Correct Option: C
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.