Physics

Electrostatics

299 Questions

Electrostatics deals with electric charges, fields, and potentials at rest. It is a crucial topic for physics sections in engineering and civil services competitive examinations. Review these questions to build a strong understanding of Coulomb law, electric dipoles, Gauss law, and electric flux.

Electric field and potentialElectric dipole momentGauss Law applicationsCoulomb force calculationsCharge distribution on spheresEquipotential surfaces

Electrostatics Questions

Multiple choice physics static electricity properties of charges charge properties of charge

Which of the following charges is/are impossible?

  1. $4.8 \times 10^{-18}C$
  2. $5.8 \times 10^{-18}C$
  3. $12.8 \times 10^{-18}C$
  4. $20.8 \times 10^{-18}C$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
From $Q=ne$,
where $Q =$ total charge
$n=$ number of electrons
$e=$ charge on one electron 
So, only that charge is possible for which charge is whole multiple of $1.6\times 10^{-19}$ (i.e, charge on one electron).
We can see that multiplying $1.6\times 10^{-19}$ with $30$ gives $A$
Multiplying $1.6\times 10^{-19}$ with $80$ gives $C$
 Multiplying $1.6\times 10^{-19}$ with $130$ gives $D$
We can see that a, c and d are multiple of charge $1.6\times 10^{-19}\:C$.
Only $5.8\times 10^{-18}\: C$ given in B) option is not a multiple of $1.6\times 10^{-19}\:C$. 

Multiple choice physics static electricity properties of charges charge properties of charge

If a conductor has $10^8$ number of electrons , then the total charge of the conductor is:

  1. $+1.6 \times 10^{-19}$ C
  2. $-1.6 \times 10^{-19}$ C
  3. $+1.6 \times 10^{-11}$ C
  4. $-1.6 \times 10^{-11}$ C
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Any charge exists in discrete lumps or packets of a certain minimum charge e where e is the charge of an electron. According to quantization of charge, the charge on a body can be only an integral multiple of charge on the electron i.e., $q = ne$ where n = 1, 2, 3 and $e=1.6\times { 10 }^{ -19 }$ C.

So, for the given case, $q=10^8 \times (-1.6 \times 10^{-19})$ C$=-1.6 \times 10^{-11}$ C.

Multiple choice physics static electricity properties of charges charge properties of charge

A spherical metal shell $A$ of radius ${R} _{A}$ and a solid metal sphere $B$ of radius ${R} _{8}\left( <{ R } _{ A } \right)$ are kept far apart and each is given charge $+Q$. Now they are connected by a thin metal wire. Then 

  1. ${ E } _{ A }^{ inside }=0$
  2. $\quad { Q } _{ A }>{ Q } _{ B }$
  3. $\dfrac { { \sigma } _{ A } }{ { \sigma } _{ B } } =\dfrac { { R } _{ B } }{ R _{ A } }$
  4. ${ E } _{ A }^{ on\quad surface }<{ E } _{ B }^{ on\quad surface }$
Reveal answer Fill a bubble to check yourself
A,B,C,D Correct answer
Explanation
Electric field inside a spherical metallic shell with charge on surface $=0$
$\therefore (a)$ is correct
On connecting Both with wise
Electric potential will be equal say $V$
$\therefore \dfrac{1}{4\pi Co}\dfrac{Q _A}{R _A}=\dfrac{1}{4\pi Co}\dfrac{Q _B}{R _B}=V$
as $R _A> R _B\therefore Q _A > Q _B$ Hence $(b)$ is correct
as $\dfrac{\sigma _A}{\sigma _B}=\dfrac{Q _B}{4\pi R _{B}^{2}}=\dfrac{R^{2}B}{R^{2}A}\times \dfrac{4\pi Co R _{A}V}{4\pi Co R _{A}R}$
$\dfrac{\sigma A}{\sigma B}=\dfrac{R _B}{R _A}$             $(C)$ is correct
Also $E _{A}=\dfrac{\sigma _A}{\sigma _B}=\dfrac{R _B}{R _A}<1\therefore E _A < E _B$
Hence $(d)$ is correct
Multiple choice physics static electricity properties of charges charge properties of charge

All free electric charges can be 
($e=$ single unit of charge i.e. the magnitude of charge on electron )

  1. odd multiples of $e$
  2. fractional multiples of $e$
  3. even multiples of $e$
  4. negative multiples of $e$
Reveal answer Fill a bubble to check yourself
A,C,D Correct answer
Explanation

Charges are acquired by either gain or loss of electrons .

And electron transfer can occur only in form of integers, fraction of electron can't be shared.

Hence, charge on a body can be positive or negative integral multiple of $e$.

Answer-(A),(C),(D)

Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

A dipole of dipole moment p is kept at the centre of a ring of radius R and charge Q. The dipole moment has direction along the axis of the ring. The resultant force on the ring due to the dipole is

  1. zero
  2. $\frac{k P Q}{R^3}$
  3. $\frac{2k P Q}{R^3}$
  4. $\frac{k P Q}{R^3}$ only if the charge is uniformly distributed on the ring
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A dipole at the center of a ring produces a field that is symmetric. The force on a charge element dq of the ring is dF = dq * E_dipole. Due to the symmetry of the dipole field and the ring, the net force integrates to zero.

Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

An electric dipole is placed at an angle of ${30}^{o}$ with an electric field of intensity $2 \times { 10 }^{ 5 }N\quad { C }^{ -1 }$. It experiences a torque equal to $4 \ N$ $m$. The charge on the dipole of the dipole length is $2 \ cm$ is

  1. $8 \ mC$
  2. $4 \ mC$
  3. $2 \ mC$
  4. $6 \ mC$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here $E=2\times { 10 }^{ 5 }N{ C }^{ -1 },l=2cm,\tau =4Nm\quad $
Torque $\vec { \tau  } =\vec { p } \times \vec { E } =pE\sin { \theta  } $
$\therefore 4=p\times 2\times { 10 }^{ 5 }\times \sin { { 30 }^{ o } } $
or $p=4\times { 10 }^{ -5 }Cm$
$\therefore$ Charge $q=\cfrac { p }{ l } =\cfrac { 4\times { 10 }^{ -5 }Cm }{ 0.02m } =2\times { 10 }^{ -3 }C=2mC$

Multiple choice

What is the Debye length?

  1. The distance from a charged surface at which the electrostatic potential is reduced to 1/e of its value at the surface

  2. The distance from a charged surface at which the electrostatic potential is reduced to 1/2 of its value at the surface

  3. The distance from a charged surface at which the electrostatic potential is reduced to 1/4 of its value at the surface

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

The Debye length is the distance from a charged surface at which the electrostatic potential is reduced to 1/e of its value at the surface.

Multiple choice

What is the relationship between the Faraday constant and the Avogadro constant?

  1. The Faraday constant is equal to the Avogadro constant multiplied by the charge of an electron.

  2. The Faraday constant is equal to the Avogadro constant divided by the charge of an electron.

  3. The Faraday constant is equal to the Avogadro constant squared.

  4. The Faraday constant is equal to the Avogadro constant cubed.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Faraday constant is related to the Avogadro constant by the equation F = N_A * e, where F is the Faraday constant, N_A is the Avogadro constant, and e is the charge of an electron.

Multiple choice

What is the electric charge of a neutrino?

  1. +1

  2. 0

  3. -1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Neutrinos have no electric charge, making them electrically neutral particles.

Multiple choice

In electromagnetism, what is the relationship between electric field and electric potential?

  1. Electric field is the gradient of electric potential

  2. Electric potential is the integral of electric field

  3. Electric field is perpendicular to electric potential

  4. Electric potential is proportional to electric field
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In electromagnetism, the electric field is the gradient of the electric potential, which means that the electric field points in the direction of the greatest rate of change of the electric potential.

Multiple choice

In electromagnetism, what is the relationship between electric field and electric displacement?

  1. Electric field is the gradient of electric displacement

  2. Electric displacement is the integral of electric field

  3. Electric field is perpendicular to electric displacement

  4. Electric displacement is proportional to electric field
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In electromagnetism, the electric displacement is proportional to the electric field, which means that the electric displacement increases as the electric field strength increases.

Multiple choice

What is the relationship between electric field and electric potential?

  1. Electric field is the gradient of electric potential

  2. Electric potential is the gradient of electric field

  3. Electric field and electric potential are independent of each other

  4. Electric field and electric potential are inversely proportional
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The electric field is the gradient of the electric potential, which means that the electric field points in the direction of the greatest rate of change of the electric potential.

Multiple choice

What is the formula for the electric force between two charges?

  1. $$F_e = kq_1q_2/r^2$$
  2. $$F_e = kq_1q_2r^2$$
  3. $$F_e = kq_1/r^2$$
  4. $$F_e = kq_2/r^2$$
  5. $$F_e = kq_1q_2r$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for the electric force between two charges is $$F_e = kq_1q_2/r^2$$. Where k is the Coulomb constant, q_1 and q_2 are the charges of the two objects, and r is the distance between the two objects.

Multiple choice

What is the formula for the electric potential at a point due to a point charge?

  1. $$V = kq/r$$
  2. $$V = kq^2/r$$
  3. $$V = kq/r^2$$
  4. $$V = kq^2/r^2$$
  5. $$V = kqr$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for the electric potential at a point due to a point charge is $$V = kq/r$$. Where k is the Coulomb constant, q is the charge of the point charge, and r is the distance between the point charge and the point at which the electric potential is being measured.