QBManager

PHXII01:ELECTRIC CHARGES AND FIELDS

358159 Two charges each of magnitude $0.01 C$ and separated by a distance of $0.4 m m$ constitute an electric dipole.If the dipole is placed in an uniform electric field ' $\vec{E}$ ' of $10 d y n e / C$ making $30^{\circ}$ angle with $\vec{E}$ , the magnitude of torque acting on dipole is

1

1.0 \times 10^{- 8} N m

2

1.5 \times 10^{- 9} N m

3

4.0 \times 10^{- 10} N m

4

2.0 \times 10^{- 10} N m

Explanation:

Given, $q = 0.01 C, l = 0.4 m m = 0.4 \times 10^{- 3} m$
Dipole moment, $p = q (l)$
$= 0.01 \times 0.4 \times 10^{- 3} = 4 \times 10^{- 6} C - m$
$E = 10 d y n e / C = 10 \times 10^{- 5} N / C$
$= 10^{- 4} N / C$
Torque acting on the dipole is
$τ = p E \sin θ$ ,
where $θ$ is the angle between $\vec{P}$ and $\vec{E}$ . $= 4 \times 10^{- 6} \times 10^{- 4} \times \sin 30^{\circ}$
$= 4 \times 10^{- 10} \times \frac{1}{2}$
$= 2 \times 10^{- 10} N - m$

Jee - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358160 An electric dipole is formed by two particles fixed at the ends of a light rigid rod of length $l$ . The mass of each particle is $m$ and charges are $- q a n d + q$ . The system is suspended by a torsionless thread in an electric field of intensity $E$ such that the dipole axis is parallel to the field. If it is slightly displaced, the period of angular motion is

1

\infty

2

2 π \sqrt{\frac{m l}{q E}}

3

2 π \sqrt{\frac{m l}{2 q E}}

4

\frac{1}{2 π} \sqrt{\frac{m l}{4 q E}}

Explanation:

The torque on the dipole is
$τ = p E \sin θ$
$τ = I α$
$I α = p E θ (F o r s m a l l θ)$
The moment of inertia is
$I = 2 (m {(\frac{l}{2})}^{2}) = \frac{m l^{2}}{2}$
$∴$ Time period $= 2 π \sqrt{\frac{I}{p E}} = 2 π \sqrt{\frac{m l}{2 q E}}$

PHXII01:ELECTRIC CHARGES AND FIELDS

358161 An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $4 \times 10^{5} N C^{- 1}$ , It experiences a torque of $8 N - m$ . The charge on the dipole, if the dipole length is 4 $c m$ will be

1

8 m C

2

4 m C

3

2 μ C

4

1 m C

Explanation:

Torque, $\vec{τ} = \vec{p} \times \vec{E} = p E \sin θ$
$8 = p \times 4 \times 10^{5} \times \sin 30^{\circ}$
$\Rightarrow p = 4 \times 10^{- 5} C - m$
Dipole moment, $p = q \times l$
$q = \frac{p}{l} = \frac{4 \times 10^{- 5}}{0.04} = 1 \times 10^{- 3} C = 1 m C$

PHXII01:ELECTRIC CHARGES AND FIELDS

358162 An electric dipole is situated in an electric field of uniform intensity $E$ whose dipole moment is $p$ and moment of inertia is $I$ . If the dipole is displaced slightly from the equilibrium position, then the time period of its oscillation is

1

2 π \sqrt{\frac{I}{p E}}

2

π \sqrt{\frac{I}{p E}}

3

\sqrt{\frac{I}{p E}}

4

\sqrt{\frac{p E}{I}}

Explanation:

As, torque i.e., $τ = p E \sin θ = I α$
For small $θ, α = \frac{- p E}{I} θ$ (As $α$ and $θ$ are opposite)
$ω = \sqrt{\frac{p E}{I}}$
$T = \frac{2 π}{ω} = 2 π \sqrt{\frac{I}{p E}}$

PHXII01:ELECTRIC CHARGES AND FIELDS

358159 Two charges each of magnitude $0.01 C$ and separated by a distance of $0.4 m m$ constitute an electric dipole.If the dipole is placed in an uniform electric field ' $\vec{E}$ ' of $10 d y n e / C$ making $30^{\circ}$ angle with $\vec{E}$ , the magnitude of torque acting on dipole is

1

1.0 \times 10^{- 8} N m

2

1.5 \times 10^{- 9} N m

3

4.0 \times 10^{- 10} N m

4

2.0 \times 10^{- 10} N m

Explanation:

Given, $q = 0.01 C, l = 0.4 m m = 0.4 \times 10^{- 3} m$
Dipole moment, $p = q (l)$
$= 0.01 \times 0.4 \times 10^{- 3} = 4 \times 10^{- 6} C - m$
$E = 10 d y n e / C = 10 \times 10^{- 5} N / C$
$= 10^{- 4} N / C$
Torque acting on the dipole is
$τ = p E \sin θ$ ,
where $θ$ is the angle between $\vec{P}$ and $\vec{E}$ . $= 4 \times 10^{- 6} \times 10^{- 4} \times \sin 30^{\circ}$
$= 4 \times 10^{- 10} \times \frac{1}{2}$
$= 2 \times 10^{- 10} N - m$

Jee - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358160 An electric dipole is formed by two particles fixed at the ends of a light rigid rod of length $l$ . The mass of each particle is $m$ and charges are $- q a n d + q$ . The system is suspended by a torsionless thread in an electric field of intensity $E$ such that the dipole axis is parallel to the field. If it is slightly displaced, the period of angular motion is

1

\infty

2

2 π \sqrt{\frac{m l}{q E}}

3

2 π \sqrt{\frac{m l}{2 q E}}

4

\frac{1}{2 π} \sqrt{\frac{m l}{4 q E}}

Explanation:

The torque on the dipole is
$τ = p E \sin θ$
$τ = I α$
$I α = p E θ (F o r s m a l l θ)$
The moment of inertia is
$I = 2 (m {(\frac{l}{2})}^{2}) = \frac{m l^{2}}{2}$
$∴$ Time period $= 2 π \sqrt{\frac{I}{p E}} = 2 π \sqrt{\frac{m l}{2 q E}}$

PHXII01:ELECTRIC CHARGES AND FIELDS

358161 An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $4 \times 10^{5} N C^{- 1}$ , It experiences a torque of $8 N - m$ . The charge on the dipole, if the dipole length is 4 $c m$ will be

1

8 m C

2

4 m C

3

2 μ C

4

1 m C

Explanation:

Torque, $\vec{τ} = \vec{p} \times \vec{E} = p E \sin θ$
$8 = p \times 4 \times 10^{5} \times \sin 30^{\circ}$
$\Rightarrow p = 4 \times 10^{- 5} C - m$
Dipole moment, $p = q \times l$
$q = \frac{p}{l} = \frac{4 \times 10^{- 5}}{0.04} = 1 \times 10^{- 3} C = 1 m C$

PHXII01:ELECTRIC CHARGES AND FIELDS

358162 An electric dipole is situated in an electric field of uniform intensity $E$ whose dipole moment is $p$ and moment of inertia is $I$ . If the dipole is displaced slightly from the equilibrium position, then the time period of its oscillation is

1

2 π \sqrt{\frac{I}{p E}}

2

π \sqrt{\frac{I}{p E}}

3

\sqrt{\frac{I}{p E}}

4

\sqrt{\frac{p E}{I}}

Explanation:

As, torque i.e., $τ = p E \sin θ = I α$
For small $θ, α = \frac{- p E}{I} θ$ (As $α$ and $θ$ are opposite)
$ω = \sqrt{\frac{p E}{I}}$
$T = \frac{2 π}{ω} = 2 π \sqrt{\frac{I}{p E}}$

PHXII01:ELECTRIC CHARGES AND FIELDS

358159 Two charges each of magnitude $0.01 C$ and separated by a distance of $0.4 m m$ constitute an electric dipole.If the dipole is placed in an uniform electric field ' $\vec{E}$ ' of $10 d y n e / C$ making $30^{\circ}$ angle with $\vec{E}$ , the magnitude of torque acting on dipole is

1

1.0 \times 10^{- 8} N m

2

1.5 \times 10^{- 9} N m

3

4.0 \times 10^{- 10} N m

4

2.0 \times 10^{- 10} N m

Explanation:

Given, $q = 0.01 C, l = 0.4 m m = 0.4 \times 10^{- 3} m$
Dipole moment, $p = q (l)$
$= 0.01 \times 0.4 \times 10^{- 3} = 4 \times 10^{- 6} C - m$
$E = 10 d y n e / C = 10 \times 10^{- 5} N / C$
$= 10^{- 4} N / C$
Torque acting on the dipole is
$τ = p E \sin θ$ ,
where $θ$ is the angle between $\vec{P}$ and $\vec{E}$ . $= 4 \times 10^{- 6} \times 10^{- 4} \times \sin 30^{\circ}$
$= 4 \times 10^{- 10} \times \frac{1}{2}$
$= 2 \times 10^{- 10} N - m$

Jee - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358160 An electric dipole is formed by two particles fixed at the ends of a light rigid rod of length $l$ . The mass of each particle is $m$ and charges are $- q a n d + q$ . The system is suspended by a torsionless thread in an electric field of intensity $E$ such that the dipole axis is parallel to the field. If it is slightly displaced, the period of angular motion is

1

\infty

2

2 π \sqrt{\frac{m l}{q E}}

3

2 π \sqrt{\frac{m l}{2 q E}}

4

\frac{1}{2 π} \sqrt{\frac{m l}{4 q E}}

Explanation:

The torque on the dipole is
$τ = p E \sin θ$
$τ = I α$
$I α = p E θ (F o r s m a l l θ)$
The moment of inertia is
$I = 2 (m {(\frac{l}{2})}^{2}) = \frac{m l^{2}}{2}$
$∴$ Time period $= 2 π \sqrt{\frac{I}{p E}} = 2 π \sqrt{\frac{m l}{2 q E}}$

PHXII01:ELECTRIC CHARGES AND FIELDS

358161 An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $4 \times 10^{5} N C^{- 1}$ , It experiences a torque of $8 N - m$ . The charge on the dipole, if the dipole length is 4 $c m$ will be

1

8 m C

2

4 m C

3

2 μ C

4

1 m C

Explanation:

Torque, $\vec{τ} = \vec{p} \times \vec{E} = p E \sin θ$
$8 = p \times 4 \times 10^{5} \times \sin 30^{\circ}$
$\Rightarrow p = 4 \times 10^{- 5} C - m$
Dipole moment, $p = q \times l$
$q = \frac{p}{l} = \frac{4 \times 10^{- 5}}{0.04} = 1 \times 10^{- 3} C = 1 m C$

PHXII01:ELECTRIC CHARGES AND FIELDS

358162 An electric dipole is situated in an electric field of uniform intensity $E$ whose dipole moment is $p$ and moment of inertia is $I$ . If the dipole is displaced slightly from the equilibrium position, then the time period of its oscillation is

1

2 π \sqrt{\frac{I}{p E}}

2

π \sqrt{\frac{I}{p E}}

3

\sqrt{\frac{I}{p E}}

4

\sqrt{\frac{p E}{I}}

Explanation:

As, torque i.e., $τ = p E \sin θ = I α$
For small $θ, α = \frac{- p E}{I} θ$ (As $α$ and $θ$ are opposite)
$ω = \sqrt{\frac{p E}{I}}$
$T = \frac{2 π}{ω} = 2 π \sqrt{\frac{I}{p E}}$

PHXII01:ELECTRIC CHARGES AND FIELDS

358159 Two charges each of magnitude $0.01 C$ and separated by a distance of $0.4 m m$ constitute an electric dipole.If the dipole is placed in an uniform electric field ' $\vec{E}$ ' of $10 d y n e / C$ making $30^{\circ}$ angle with $\vec{E}$ , the magnitude of torque acting on dipole is

1

1.0 \times 10^{- 8} N m

2

1.5 \times 10^{- 9} N m

3

4.0 \times 10^{- 10} N m

4

2.0 \times 10^{- 10} N m

Explanation:

Given, $q = 0.01 C, l = 0.4 m m = 0.4 \times 10^{- 3} m$
Dipole moment, $p = q (l)$
$= 0.01 \times 0.4 \times 10^{- 3} = 4 \times 10^{- 6} C - m$
$E = 10 d y n e / C = 10 \times 10^{- 5} N / C$
$= 10^{- 4} N / C$
Torque acting on the dipole is
$τ = p E \sin θ$ ,
where $θ$ is the angle between $\vec{P}$ and $\vec{E}$ . $= 4 \times 10^{- 6} \times 10^{- 4} \times \sin 30^{\circ}$
$= 4 \times 10^{- 10} \times \frac{1}{2}$
$= 2 \times 10^{- 10} N - m$

Jee - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358160 An electric dipole is formed by two particles fixed at the ends of a light rigid rod of length $l$ . The mass of each particle is $m$ and charges are $- q a n d + q$ . The system is suspended by a torsionless thread in an electric field of intensity $E$ such that the dipole axis is parallel to the field. If it is slightly displaced, the period of angular motion is

1

\infty

2

2 π \sqrt{\frac{m l}{q E}}

3

2 π \sqrt{\frac{m l}{2 q E}}

4

\frac{1}{2 π} \sqrt{\frac{m l}{4 q E}}

Explanation:

The torque on the dipole is
$τ = p E \sin θ$
$τ = I α$
$I α = p E θ (F o r s m a l l θ)$
The moment of inertia is
$I = 2 (m {(\frac{l}{2})}^{2}) = \frac{m l^{2}}{2}$
$∴$ Time period $= 2 π \sqrt{\frac{I}{p E}} = 2 π \sqrt{\frac{m l}{2 q E}}$

PHXII01:ELECTRIC CHARGES AND FIELDS

358161 An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $4 \times 10^{5} N C^{- 1}$ , It experiences a torque of $8 N - m$ . The charge on the dipole, if the dipole length is 4 $c m$ will be

1

8 m C

2

4 m C

3

2 μ C

4

1 m C

Explanation:

Torque, $\vec{τ} = \vec{p} \times \vec{E} = p E \sin θ$
$8 = p \times 4 \times 10^{5} \times \sin 30^{\circ}$
$\Rightarrow p = 4 \times 10^{- 5} C - m$
Dipole moment, $p = q \times l$
$q = \frac{p}{l} = \frac{4 \times 10^{- 5}}{0.04} = 1 \times 10^{- 3} C = 1 m C$

PHXII01:ELECTRIC CHARGES AND FIELDS

358162 An electric dipole is situated in an electric field of uniform intensity $E$ whose dipole moment is $p$ and moment of inertia is $I$ . If the dipole is displaced slightly from the equilibrium position, then the time period of its oscillation is

1

2 π \sqrt{\frac{I}{p E}}

2

π \sqrt{\frac{I}{p E}}

3

\sqrt{\frac{I}{p E}}

4

\sqrt{\frac{p E}{I}}

Explanation:

As, torque i.e., $τ = p E \sin θ = I α$
For small $θ, α = \frac{- p E}{I} θ$ (As $α$ and $θ$ are opposite)
$ω = \sqrt{\frac{p E}{I}}$
$T = \frac{2 π}{ω} = 2 π \sqrt{\frac{I}{p E}}$

Explanation:

Explanation:

Explanation:

Explanation:

Question Bank Series

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Question Bank Series