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PHXII01:ELECTRIC CHARGES AND FIELDS

358133 An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $2 \times 10^{5} N C^{- 1}$ . It experiences a torque equal to $4 N m$ . Calculate the magnitude of charge on the dipole, if the dipole length is $2 c m$ .

1

6 m C

2

4 m C

3

2 m C

4

8 m C

Explanation:

$τ$ on a dipole $= \vec{p} \times \vec{E}$
$\Rightarrow τ = p E \sin θ$
$\Rightarrow 4 = q \times l \times E \times \sin 30^{\circ}$
$\Rightarrow 4 = q \times 2 \times 10^{- 2} \times 2 \times 10^{5} \times \frac{1}{2}$
$\Rightarrow q = 2 \times 10^{- 3} \Rightarrow q = 2 m C$
Correct option is (3).

NEET - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358134 Two point charges $- q$ and $+ q$ are placed at a distance of $L$ , as shown in the figure.
The magnitude of electric field intensity at a distance $R (R >> L)$ varies as
supporting img

1

\frac{1}{R^{3}}

2

\frac{1}{R^{4}}

3

\frac{1}{R^{6}}

4

\frac{1}{R^{2}}

Explanation:

It is electric dipole so,at large distance electric field intensity
$E = \frac{K p}{R^{3}} \sqrt{1 + 3 \cos^{2} θ}$
$M$ is the point where field $E$ is written
Here, $k = \frac{1}{4 π ε_{0}}$
$p = q (2 a)$
$∴ E \propto \frac{1}{R^{3}}$
supporting img

NEET - 2022

PHXII01:ELECTRIC CHARGES AND FIELDS

358135 The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as

1

\frac{1}{r^{2}}

2

\frac{1}{r}

3

\frac{1}{r^{3}}

4

r

Explanation:

The electric field is given by
$E = \frac{K p}{r^{3}} \sqrt{1 + 3 \cos^{2} θ}$ For equatorial plane,
$θ = 90^{\circ}$
$E = \frac{K p}{r^{3}} \Rightarrow E \propto \frac{1}{r^{3}}$

Jee - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358136 Assertion :
The electric field due to a dipole on its axial line at a distance $r$ is $E$ . Then, electric field due to the same dipole on the equatorial line and at the same distance will be $\frac{E}{2}$
Reason :
Electric field due to dipole varies inversely as the square of distance on axial line.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The assertion correctly explains the relation between the electric fields on the axial and equatorial lines of a dipole. $E_{axial} = \frac{2 \vec{p}}{4 π E_{0} r^{3}}$
Here $C$ is centre of dipole
supporting img
Here $P$ is point where field is calculated
${\vec{E}}_{axial} \propto \frac{1}{r^{3}} \Rightarrow$ Reason is false
So correct option is (3).

PHXII01:ELECTRIC CHARGES AND FIELDS

358137 Which of the following statements about dipole moment is not true?

1 The unit of dipole moment is

C

m

.

2 The dimensions of dipole moment is [LTA].

3 Dipole moment is a vector quantity and directed from negative to positive charge.

4 Dipole moment is a scalar quantity

Explanation:

Dipole moment is a vector quantity and it is in the direction from $- q t o q$

PHXII01:ELECTRIC CHARGES AND FIELDS

358133 An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $2 \times 10^{5} N C^{- 1}$ . It experiences a torque equal to $4 N m$ . Calculate the magnitude of charge on the dipole, if the dipole length is $2 c m$ .

1

6 m C

2

4 m C

3

2 m C

4

8 m C

Explanation:

$τ$ on a dipole $= \vec{p} \times \vec{E}$
$\Rightarrow τ = p E \sin θ$
$\Rightarrow 4 = q \times l \times E \times \sin 30^{\circ}$
$\Rightarrow 4 = q \times 2 \times 10^{- 2} \times 2 \times 10^{5} \times \frac{1}{2}$
$\Rightarrow q = 2 \times 10^{- 3} \Rightarrow q = 2 m C$
Correct option is (3).

NEET - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358134 Two point charges $- q$ and $+ q$ are placed at a distance of $L$ , as shown in the figure.
The magnitude of electric field intensity at a distance $R (R >> L)$ varies as
supporting img

1

\frac{1}{R^{3}}

2

\frac{1}{R^{4}}

3

\frac{1}{R^{6}}

4

\frac{1}{R^{2}}

Explanation:

It is electric dipole so,at large distance electric field intensity
$E = \frac{K p}{R^{3}} \sqrt{1 + 3 \cos^{2} θ}$
$M$ is the point where field $E$ is written
Here, $k = \frac{1}{4 π ε_{0}}$
$p = q (2 a)$
$∴ E \propto \frac{1}{R^{3}}$
supporting img

NEET - 2022

PHXII01:ELECTRIC CHARGES AND FIELDS

358135 The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as

1

\frac{1}{r^{2}}

2

\frac{1}{r}

3

\frac{1}{r^{3}}

4

r

Explanation:

The electric field is given by
$E = \frac{K p}{r^{3}} \sqrt{1 + 3 \cos^{2} θ}$ For equatorial plane,
$θ = 90^{\circ}$
$E = \frac{K p}{r^{3}} \Rightarrow E \propto \frac{1}{r^{3}}$

Jee - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358136 Assertion :
The electric field due to a dipole on its axial line at a distance $r$ is $E$ . Then, electric field due to the same dipole on the equatorial line and at the same distance will be $\frac{E}{2}$
Reason :
Electric field due to dipole varies inversely as the square of distance on axial line.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The assertion correctly explains the relation between the electric fields on the axial and equatorial lines of a dipole. $E_{axial} = \frac{2 \vec{p}}{4 π E_{0} r^{3}}$
Here $C$ is centre of dipole
supporting img
Here $P$ is point where field is calculated
${\vec{E}}_{axial} \propto \frac{1}{r^{3}} \Rightarrow$ Reason is false
So correct option is (3).

PHXII01:ELECTRIC CHARGES AND FIELDS

358137 Which of the following statements about dipole moment is not true?

1 The unit of dipole moment is

C

m

.

2 The dimensions of dipole moment is [LTA].

3 Dipole moment is a vector quantity and directed from negative to positive charge.

4 Dipole moment is a scalar quantity

Explanation:

Dipole moment is a vector quantity and it is in the direction from $- q t o q$

PHXII01:ELECTRIC CHARGES AND FIELDS

358133 An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $2 \times 10^{5} N C^{- 1}$ . It experiences a torque equal to $4 N m$ . Calculate the magnitude of charge on the dipole, if the dipole length is $2 c m$ .

1

6 m C

2

4 m C

3

2 m C

4

8 m C

Explanation:

$τ$ on a dipole $= \vec{p} \times \vec{E}$
$\Rightarrow τ = p E \sin θ$
$\Rightarrow 4 = q \times l \times E \times \sin 30^{\circ}$
$\Rightarrow 4 = q \times 2 \times 10^{- 2} \times 2 \times 10^{5} \times \frac{1}{2}$
$\Rightarrow q = 2 \times 10^{- 3} \Rightarrow q = 2 m C$
Correct option is (3).

NEET - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358134 Two point charges $- q$ and $+ q$ are placed at a distance of $L$ , as shown in the figure.
The magnitude of electric field intensity at a distance $R (R >> L)$ varies as
supporting img

1

\frac{1}{R^{3}}

2

\frac{1}{R^{4}}

3

\frac{1}{R^{6}}

4

\frac{1}{R^{2}}

Explanation:

It is electric dipole so,at large distance electric field intensity
$E = \frac{K p}{R^{3}} \sqrt{1 + 3 \cos^{2} θ}$
$M$ is the point where field $E$ is written
Here, $k = \frac{1}{4 π ε_{0}}$
$p = q (2 a)$
$∴ E \propto \frac{1}{R^{3}}$
supporting img

NEET - 2022

PHXII01:ELECTRIC CHARGES AND FIELDS

358135 The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as

1

\frac{1}{r^{2}}

2

\frac{1}{r}

3

\frac{1}{r^{3}}

4

r

Explanation:

The electric field is given by
$E = \frac{K p}{r^{3}} \sqrt{1 + 3 \cos^{2} θ}$ For equatorial plane,
$θ = 90^{\circ}$
$E = \frac{K p}{r^{3}} \Rightarrow E \propto \frac{1}{r^{3}}$

Jee - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358136 Assertion :
The electric field due to a dipole on its axial line at a distance $r$ is $E$ . Then, electric field due to the same dipole on the equatorial line and at the same distance will be $\frac{E}{2}$
Reason :
Electric field due to dipole varies inversely as the square of distance on axial line.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The assertion correctly explains the relation between the electric fields on the axial and equatorial lines of a dipole. $E_{axial} = \frac{2 \vec{p}}{4 π E_{0} r^{3}}$
Here $C$ is centre of dipole
supporting img
Here $P$ is point where field is calculated
${\vec{E}}_{axial} \propto \frac{1}{r^{3}} \Rightarrow$ Reason is false
So correct option is (3).

PHXII01:ELECTRIC CHARGES AND FIELDS

358137 Which of the following statements about dipole moment is not true?

1 The unit of dipole moment is

C

m

.

2 The dimensions of dipole moment is [LTA].

3 Dipole moment is a vector quantity and directed from negative to positive charge.

4 Dipole moment is a scalar quantity

Explanation:

Dipole moment is a vector quantity and it is in the direction from $- q t o q$

PHXII01:ELECTRIC CHARGES AND FIELDS

358133 An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $2 \times 10^{5} N C^{- 1}$ . It experiences a torque equal to $4 N m$ . Calculate the magnitude of charge on the dipole, if the dipole length is $2 c m$ .

1

6 m C

2

4 m C

3

2 m C

4

8 m C

Explanation:

$τ$ on a dipole $= \vec{p} \times \vec{E}$
$\Rightarrow τ = p E \sin θ$
$\Rightarrow 4 = q \times l \times E \times \sin 30^{\circ}$
$\Rightarrow 4 = q \times 2 \times 10^{- 2} \times 2 \times 10^{5} \times \frac{1}{2}$
$\Rightarrow q = 2 \times 10^{- 3} \Rightarrow q = 2 m C$
Correct option is (3).

NEET - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358134 Two point charges $- q$ and $+ q$ are placed at a distance of $L$ , as shown in the figure.
The magnitude of electric field intensity at a distance $R (R >> L)$ varies as
supporting img

1

\frac{1}{R^{3}}

2

\frac{1}{R^{4}}

3

\frac{1}{R^{6}}

4

\frac{1}{R^{2}}

Explanation:

It is electric dipole so,at large distance electric field intensity
$E = \frac{K p}{R^{3}} \sqrt{1 + 3 \cos^{2} θ}$
$M$ is the point where field $E$ is written
Here, $k = \frac{1}{4 π ε_{0}}$
$p = q (2 a)$
$∴ E \propto \frac{1}{R^{3}}$
supporting img

NEET - 2022

PHXII01:ELECTRIC CHARGES AND FIELDS

358135 The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as

1

\frac{1}{r^{2}}

2

\frac{1}{r}

3

\frac{1}{r^{3}}

4

r

Explanation:

The electric field is given by
$E = \frac{K p}{r^{3}} \sqrt{1 + 3 \cos^{2} θ}$ For equatorial plane,
$θ = 90^{\circ}$
$E = \frac{K p}{r^{3}} \Rightarrow E \propto \frac{1}{r^{3}}$

Jee - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358136 Assertion :
The electric field due to a dipole on its axial line at a distance $r$ is $E$ . Then, electric field due to the same dipole on the equatorial line and at the same distance will be $\frac{E}{2}$
Reason :
Electric field due to dipole varies inversely as the square of distance on axial line.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The assertion correctly explains the relation between the electric fields on the axial and equatorial lines of a dipole. $E_{axial} = \frac{2 \vec{p}}{4 π E_{0} r^{3}}$
Here $C$ is centre of dipole
supporting img
Here $P$ is point where field is calculated
${\vec{E}}_{axial} \propto \frac{1}{r^{3}} \Rightarrow$ Reason is false
So correct option is (3).

PHXII01:ELECTRIC CHARGES AND FIELDS

358137 Which of the following statements about dipole moment is not true?

1 The unit of dipole moment is

C

m

.

2 The dimensions of dipole moment is [LTA].

3 Dipole moment is a vector quantity and directed from negative to positive charge.

4 Dipole moment is a scalar quantity

Explanation:

Dipole moment is a vector quantity and it is in the direction from $- q t o q$

PHXII01:ELECTRIC CHARGES AND FIELDS

358133 An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $2 \times 10^{5} N C^{- 1}$ . It experiences a torque equal to $4 N m$ . Calculate the magnitude of charge on the dipole, if the dipole length is $2 c m$ .

1

6 m C

2

4 m C

3

2 m C

4

8 m C

Explanation:

$τ$ on a dipole $= \vec{p} \times \vec{E}$
$\Rightarrow τ = p E \sin θ$
$\Rightarrow 4 = q \times l \times E \times \sin 30^{\circ}$
$\Rightarrow 4 = q \times 2 \times 10^{- 2} \times 2 \times 10^{5} \times \frac{1}{2}$
$\Rightarrow q = 2 \times 10^{- 3} \Rightarrow q = 2 m C$
Correct option is (3).

NEET - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358134 Two point charges $- q$ and $+ q$ are placed at a distance of $L$ , as shown in the figure.
The magnitude of electric field intensity at a distance $R (R >> L)$ varies as
supporting img

1

\frac{1}{R^{3}}

2

\frac{1}{R^{4}}

3

\frac{1}{R^{6}}

4

\frac{1}{R^{2}}

Explanation:

It is electric dipole so,at large distance electric field intensity
$E = \frac{K p}{R^{3}} \sqrt{1 + 3 \cos^{2} θ}$
$M$ is the point where field $E$ is written
Here, $k = \frac{1}{4 π ε_{0}}$
$p = q (2 a)$
$∴ E \propto \frac{1}{R^{3}}$
supporting img

NEET - 2022

PHXII01:ELECTRIC CHARGES AND FIELDS

358135 The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as

1

\frac{1}{r^{2}}

2

\frac{1}{r}

3

\frac{1}{r^{3}}

4

r

Explanation:

The electric field is given by
$E = \frac{K p}{r^{3}} \sqrt{1 + 3 \cos^{2} θ}$ For equatorial plane,
$θ = 90^{\circ}$
$E = \frac{K p}{r^{3}} \Rightarrow E \propto \frac{1}{r^{3}}$

Jee - 2023

PHXII01:ELECTRIC CHARGES AND FIELDS

358136 Assertion :
The electric field due to a dipole on its axial line at a distance $r$ is $E$ . Then, electric field due to the same dipole on the equatorial line and at the same distance will be $\frac{E}{2}$
Reason :
Electric field due to dipole varies inversely as the square of distance on axial line.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The assertion correctly explains the relation between the electric fields on the axial and equatorial lines of a dipole. $E_{axial} = \frac{2 \vec{p}}{4 π E_{0} r^{3}}$
Here $C$ is centre of dipole
supporting img
Here $P$ is point where field is calculated
${\vec{E}}_{axial} \propto \frac{1}{r^{3}} \Rightarrow$ Reason is false
So correct option is (3).

PHXII01:ELECTRIC CHARGES AND FIELDS

358137 Which of the following statements about dipole moment is not true?

1 The unit of dipole moment is

C

m

.

2 The dimensions of dipole moment is [LTA].

3 Dipole moment is a vector quantity and directed from negative to positive charge.

4 Dipole moment is a scalar quantity

Explanation:

Dipole moment is a vector quantity and it is in the direction from $- q t o q$