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Electric Dipole

Practice Questions:

Question 1: easy

The electric potential at a point due to an electric dipole is :

1. \[k(\overrightarrow{p}.\overrightarrow{r}/r^{3})\]

2. \[k(\overrightarrow{p}.\overrightarrow{r}/r^{2})\]

3. \[ k(\overrightarrow{p}\times \overrightarrow{r}/r^{3})\]

4. \[k(\overrightarrow{p}\times \overrightarrow{r}/r^{2})\]

View Answer

The electric potential \( V \) at a point \( P \) due to an electric dipole with dipole moment \( \overrightarrow{p} \) is given by:

\[
V = \frac{k \, \overrightarrow{p} \cdot \overrightarrow{r}}{r^3}
\]

Explanation:
1. Dipole Moment: The dipole moment \( \overrightarrow{p} = q \cdot d \), where \( q \) is the charge and \( d \) is the separation between charges.

2. Position Vector \( \overrightarrow{r} \): This is the vector from the center of the dipole to the point \( P \).

3. Dot Product: The potential depends on the angle between \( \overrightarrow{p} \) and \( \overrightarrow{r} \), hence \( \overrightarrow{p} \cdot \overrightarrow{r} = p r \cos \theta \).

4. Result: The formula is:
\[
V = \frac{k (\overrightarrow{p} \cdot \overrightarrow{r})}{r^3}
\]

This matches the correct answer:
\[
V = \frac{k (\overrightarrow{p} \cdot \overrightarrow{r})}{r^3}
\]

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Question 2: easy

An electric dipole consisting of two opposite charges of \( 2 \times 10^{-6}\text{ C} \) each separated by a distance of 3 cm is placed in an electric field of \( 2 \times 10^5\text{ N/C} \). The maximum torque on the dipole will be:

1. \( 12 \times 10^{-1}\text{ Nm} \)

2. \( 12 \times 10^{-3}\text{ Nm} \)

3. \( 24 \times 10^{-1}\text{ Nm} \)

4. \( 24 \times 10^{-3}\text{ Nm} \)

View Answer

Maximum torque on a dipole in a uniform electric field is \( \tau_{max} = pE = (q \cdot 2l)E \). Substituting the given values: \( \tau_{max} = (2 \times 10^{-6}\text{ C} \times 0.03\text{ m}) \times (2 \times 10^5\text{ N/C}) = 12 \times 10^{-3}\text{ Nm} \).

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Question 3: easy

An electric dipole has the magnitude of its charge as \(q\) and its dipole moment is \(p\). It is placed in a uniform electric field \(E\). If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively:

1. \(2qE\) and minimum

2. \(qE\) and \(pE\)

3. Zero and minimum

4. Zero and maximum

View Answer

In a uniform electric field, the net force on a dipole is always zero. The potential energy is \(U = -pE \cos(0^\circ) = -pE\), which is the minimum potential energy.

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Question 4: easy

An electric dipole of dipole moment \(\vec{P}\) is initially aligned along a uniform electric field \(\vec{E}\). The work done in rotating it by \(90^\circ\) will be

1. \(-PE\)

2. Zero

3. \(PE\)

4. \(\frac{PE}{2}\)

View Answer

The work done in rotating a dipole in a uniform electric field is given by \(W = PE(cos\theta_1 - cos\theta_2)\). Since it is rotated from \(\theta_1 = 0^\circ\) to \(\theta_2 = 90^\circ\), \(W = PE(cos 0^\circ - cos 90^\circ) = PE\).

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Question 5: easy

Assertion (A): Angular momentum of the two dipole system is not conserved.

Reason (R): There is a net torque on the system.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

For an isolated system of two dipoles, the torques they exert on each other are internal forces. Internal torques within a system cancel each other out, leading to zero net torque on the system. Therefore, according to the conservation of angular momentum \(\frac{d\vec{L}}{dt} = \vec{\tau}_{ext}\)), if the net external torque is zero, the angular momentum of the system is conserved. Hence, both assertion (A) and reason (R) are false.

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Question 6: easy

Assertion (A): When a dipole is placed in a non- uniform electric field dipole must experience non zero force and torque.

Reason (R): Electric dipole is in stable equilibrium in non uniform electric field.

1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (3) (A) is true but (R) is false

4. (4) Both (A) and (R) are false

View Answer

In a non-uniform field, `\( +q \)` and `\( -q \)` experience different forces, leading to a net force and torque. Thus (A) is true. However, a dipole is generally not in stable equilibrium in a non-uniform field, so (R) is false.

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