QBManager

Electric Charges and Fields

267918 There point charges $+ q, - q$ and $+ q$ are placed at the vertices $P, Q$ and $R$ of an equilateral triangle as shown. If $F = \frac{1}{4 π ε_{0}} \frac{q^{2}}{r^{2}}$ , where ' $r$ ' is the side of the triangle, the force on charge at ' $P$ ' due to charges at $Q$ and $R$ is

1 F alongpositivex-direction

2 F along negative

x

-direction

3

\sqrt{2} F

along positive

x

-direction

4

\sqrt{2} F

along negative

x

-direction

Explanation:

$F_{1} = F_{2}$ and angle between them is $120^{\circ}$

Electric Charges and Fields

267919 Three point charges $+ q, + q$ and $- q$ are placed at the corners of an equilateral triangle of side ' $a$ ' . Another charge $+ Q$ is kept at the centroid. Force exerted on $Q$ is:

1

\frac{1}{4 π ε_{0}} \frac{2 q Q}{a^{2}}

2

\frac{1}{4 π ε_{0}} \frac{6 q Q}{a^{2}}

3

\frac{1}{4 π ε_{0}} \frac{8 q Q}{a^{2}}

4

\frac{1}{4 π ε_{0}} \frac{14 q Q}{a^{2}}

Explanation:

$F = {(\frac{1}{4 π ε_{0}} \frac{q}{r^{2}})}^{2}$ where $r = \frac{a}{\sqrt{3}}$

Electric Charges and Fields

267920 Three charges $- q_{1}, + q_{2}$ and $- q_{3}$ are placed as shown in fig. The $X$ -component of the force on $- q_{1}$ is proportional to

1

\frac{q_{2}}{b^{2}} - \frac{q_{3}}{a^{2}} \cos θ

2

\frac{q_{2}}{b^{2}} + \frac{q_{3}}{a^{2}} \sin θ

3

\frac{q_{2}}{b^{2}} + \frac{q_{2}}{a^{2}} \cos θ

4 $\frac{q_2}{b^2}-\frac{q_2}{a^2} \sin \theta$

Electric Charges and Fields

272130 Three charges $+ q, + 2 q$ and $+ 4 q$ are connected by strings as shown in the figure. What is ratio of tensions in the strings $A B$ and $B C$ ?

1

1 : 2

2

1 : 3

3

2 : 1

4

3 : 1

Explanation:

(b) $T_{A B} = \frac{k q \cdot 2 q}{d^{2}} + \frac{k q \cdot 4 q}{{(2 d)}^{2}} = \frac{3 k q^{2}}{d}$
$T_{B C} = \frac{k \cdot 4 q \cdot 2 q}{d^{2}} + \frac{k q \cdot 4 q}{{(2 d)}^{2}} = \frac{9 k q^{2}}{d^{2}}$

NCERT Page-12 / N-7

Electric Charges and Fields

272131 The figure shows a charge $+ q$ at point $P$ held in equilibrium in air with the help of four $+ q$ charges situated at the vertices of a square: The net electrostatic force on $q$ is given by

1 Newton's

2 Coulomb's law

3 Principle of superposition

4 Net electric flux out the position of

+ q

.

Explanation:

(c) The weight $m g$ of the charge hold in air is in equillibrium with net electrostatic force exerted by the four charges situated at the corners. The net electrostatic force is given by the vector sum of the individual forces exerted by the charges at the corners. This is principle of superposition.

NCERT Page-15/ N-12

Electric Charges and Fields

267918 There point charges $+ q, - q$ and $+ q$ are placed at the vertices $P, Q$ and $R$ of an equilateral triangle as shown. If $F = \frac{1}{4 π ε_{0}} \frac{q^{2}}{r^{2}}$ , where ' $r$ ' is the side of the triangle, the force on charge at ' $P$ ' due to charges at $Q$ and $R$ is

1 F alongpositivex-direction

2 F along negative

x

-direction

3

\sqrt{2} F

along positive

x

-direction

4

\sqrt{2} F

along negative

x

-direction

Explanation:

$F_{1} = F_{2}$ and angle between them is $120^{\circ}$

Electric Charges and Fields

267919 Three point charges $+ q, + q$ and $- q$ are placed at the corners of an equilateral triangle of side ' $a$ ' . Another charge $+ Q$ is kept at the centroid. Force exerted on $Q$ is:

1

\frac{1}{4 π ε_{0}} \frac{2 q Q}{a^{2}}

2

\frac{1}{4 π ε_{0}} \frac{6 q Q}{a^{2}}

3

\frac{1}{4 π ε_{0}} \frac{8 q Q}{a^{2}}

4

\frac{1}{4 π ε_{0}} \frac{14 q Q}{a^{2}}

Explanation:

$F = {(\frac{1}{4 π ε_{0}} \frac{q}{r^{2}})}^{2}$ where $r = \frac{a}{\sqrt{3}}$

Electric Charges and Fields

267920 Three charges $- q_{1}, + q_{2}$ and $- q_{3}$ are placed as shown in fig. The $X$ -component of the force on $- q_{1}$ is proportional to

1

\frac{q_{2}}{b^{2}} - \frac{q_{3}}{a^{2}} \cos θ

2

\frac{q_{2}}{b^{2}} + \frac{q_{3}}{a^{2}} \sin θ

3

\frac{q_{2}}{b^{2}} + \frac{q_{2}}{a^{2}} \cos θ

4 $\frac{q_2}{b^2}-\frac{q_2}{a^2} \sin \theta$

Electric Charges and Fields

272130 Three charges $+ q, + 2 q$ and $+ 4 q$ are connected by strings as shown in the figure. What is ratio of tensions in the strings $A B$ and $B C$ ?

1

1 : 2

2

1 : 3

3

2 : 1

4

3 : 1

Explanation:

(b) $T_{A B} = \frac{k q \cdot 2 q}{d^{2}} + \frac{k q \cdot 4 q}{{(2 d)}^{2}} = \frac{3 k q^{2}}{d}$
$T_{B C} = \frac{k \cdot 4 q \cdot 2 q}{d^{2}} + \frac{k q \cdot 4 q}{{(2 d)}^{2}} = \frac{9 k q^{2}}{d^{2}}$

NCERT Page-12 / N-7

Electric Charges and Fields

272131 The figure shows a charge $+ q$ at point $P$ held in equilibrium in air with the help of four $+ q$ charges situated at the vertices of a square: The net electrostatic force on $q$ is given by

1 Newton's

2 Coulomb's law

3 Principle of superposition

4 Net electric flux out the position of

+ q

.

Explanation:

(c) The weight $m g$ of the charge hold in air is in equillibrium with net electrostatic force exerted by the four charges situated at the corners. The net electrostatic force is given by the vector sum of the individual forces exerted by the charges at the corners. This is principle of superposition.

NCERT Page-15/ N-12

Electric Charges and Fields

267918 There point charges $+ q, - q$ and $+ q$ are placed at the vertices $P, Q$ and $R$ of an equilateral triangle as shown. If $F = \frac{1}{4 π ε_{0}} \frac{q^{2}}{r^{2}}$ , where ' $r$ ' is the side of the triangle, the force on charge at ' $P$ ' due to charges at $Q$ and $R$ is

1 F alongpositivex-direction

2 F along negative

x

-direction

3

\sqrt{2} F

along positive

x

-direction

4

\sqrt{2} F

along negative

x

-direction

Explanation:

$F_{1} = F_{2}$ and angle between them is $120^{\circ}$

Electric Charges and Fields

267919 Three point charges $+ q, + q$ and $- q$ are placed at the corners of an equilateral triangle of side ' $a$ ' . Another charge $+ Q$ is kept at the centroid. Force exerted on $Q$ is:

1

\frac{1}{4 π ε_{0}} \frac{2 q Q}{a^{2}}

2

\frac{1}{4 π ε_{0}} \frac{6 q Q}{a^{2}}

3

\frac{1}{4 π ε_{0}} \frac{8 q Q}{a^{2}}

4

\frac{1}{4 π ε_{0}} \frac{14 q Q}{a^{2}}

Explanation:

$F = {(\frac{1}{4 π ε_{0}} \frac{q}{r^{2}})}^{2}$ where $r = \frac{a}{\sqrt{3}}$

Electric Charges and Fields

267920 Three charges $- q_{1}, + q_{2}$ and $- q_{3}$ are placed as shown in fig. The $X$ -component of the force on $- q_{1}$ is proportional to

1

\frac{q_{2}}{b^{2}} - \frac{q_{3}}{a^{2}} \cos θ

2

\frac{q_{2}}{b^{2}} + \frac{q_{3}}{a^{2}} \sin θ

3

\frac{q_{2}}{b^{2}} + \frac{q_{2}}{a^{2}} \cos θ

4 $\frac{q_2}{b^2}-\frac{q_2}{a^2} \sin \theta$

Electric Charges and Fields

272130 Three charges $+ q, + 2 q$ and $+ 4 q$ are connected by strings as shown in the figure. What is ratio of tensions in the strings $A B$ and $B C$ ?

1

1 : 2

2

1 : 3

3

2 : 1

4

3 : 1

Explanation:

(b) $T_{A B} = \frac{k q \cdot 2 q}{d^{2}} + \frac{k q \cdot 4 q}{{(2 d)}^{2}} = \frac{3 k q^{2}}{d}$
$T_{B C} = \frac{k \cdot 4 q \cdot 2 q}{d^{2}} + \frac{k q \cdot 4 q}{{(2 d)}^{2}} = \frac{9 k q^{2}}{d^{2}}$

NCERT Page-12 / N-7

Electric Charges and Fields

272131 The figure shows a charge $+ q$ at point $P$ held in equilibrium in air with the help of four $+ q$ charges situated at the vertices of a square: The net electrostatic force on $q$ is given by

1 Newton's

2 Coulomb's law

3 Principle of superposition

4 Net electric flux out the position of

+ q

.

Explanation:

(c) The weight $m g$ of the charge hold in air is in equillibrium with net electrostatic force exerted by the four charges situated at the corners. The net electrostatic force is given by the vector sum of the individual forces exerted by the charges at the corners. This is principle of superposition.

NCERT Page-15/ N-12

Electric Charges and Fields

267918 There point charges $+ q, - q$ and $+ q$ are placed at the vertices $P, Q$ and $R$ of an equilateral triangle as shown. If $F = \frac{1}{4 π ε_{0}} \frac{q^{2}}{r^{2}}$ , where ' $r$ ' is the side of the triangle, the force on charge at ' $P$ ' due to charges at $Q$ and $R$ is

1 F alongpositivex-direction

2 F along negative

x

-direction

3

\sqrt{2} F

along positive

x

-direction

4

\sqrt{2} F

along negative

x

-direction

Explanation:

$F_{1} = F_{2}$ and angle between them is $120^{\circ}$

Electric Charges and Fields

267919 Three point charges $+ q, + q$ and $- q$ are placed at the corners of an equilateral triangle of side ' $a$ ' . Another charge $+ Q$ is kept at the centroid. Force exerted on $Q$ is:

1

\frac{1}{4 π ε_{0}} \frac{2 q Q}{a^{2}}

2

\frac{1}{4 π ε_{0}} \frac{6 q Q}{a^{2}}

3

\frac{1}{4 π ε_{0}} \frac{8 q Q}{a^{2}}

4

\frac{1}{4 π ε_{0}} \frac{14 q Q}{a^{2}}

Explanation:

$F = {(\frac{1}{4 π ε_{0}} \frac{q}{r^{2}})}^{2}$ where $r = \frac{a}{\sqrt{3}}$

Electric Charges and Fields

267920 Three charges $- q_{1}, + q_{2}$ and $- q_{3}$ are placed as shown in fig. The $X$ -component of the force on $- q_{1}$ is proportional to

1

\frac{q_{2}}{b^{2}} - \frac{q_{3}}{a^{2}} \cos θ

2

\frac{q_{2}}{b^{2}} + \frac{q_{3}}{a^{2}} \sin θ

3

\frac{q_{2}}{b^{2}} + \frac{q_{2}}{a^{2}} \cos θ

4 $\frac{q_2}{b^2}-\frac{q_2}{a^2} \sin \theta$

Electric Charges and Fields

272130 Three charges $+ q, + 2 q$ and $+ 4 q$ are connected by strings as shown in the figure. What is ratio of tensions in the strings $A B$ and $B C$ ?

1

1 : 2

2

1 : 3

3

2 : 1

4

3 : 1

Explanation:

(b) $T_{A B} = \frac{k q \cdot 2 q}{d^{2}} + \frac{k q \cdot 4 q}{{(2 d)}^{2}} = \frac{3 k q^{2}}{d}$
$T_{B C} = \frac{k \cdot 4 q \cdot 2 q}{d^{2}} + \frac{k q \cdot 4 q}{{(2 d)}^{2}} = \frac{9 k q^{2}}{d^{2}}$

NCERT Page-12 / N-7

Electric Charges and Fields

272131 The figure shows a charge $+ q$ at point $P$ held in equilibrium in air with the help of four $+ q$ charges situated at the vertices of a square: The net electrostatic force on $q$ is given by

1 Newton's

2 Coulomb's law

3 Principle of superposition

4 Net electric flux out the position of

+ q

.

Explanation:

(c) The weight $m g$ of the charge hold in air is in equillibrium with net electrostatic force exerted by the four charges situated at the corners. The net electrostatic force is given by the vector sum of the individual forces exerted by the charges at the corners. This is principle of superposition.

NCERT Page-15/ N-12

Electric Charges and Fields

267918 There point charges $+ q, - q$ and $+ q$ are placed at the vertices $P, Q$ and $R$ of an equilateral triangle as shown. If $F = \frac{1}{4 π ε_{0}} \frac{q^{2}}{r^{2}}$ , where ' $r$ ' is the side of the triangle, the force on charge at ' $P$ ' due to charges at $Q$ and $R$ is

1 F alongpositivex-direction

2 F along negative

x

-direction

3

\sqrt{2} F

along positive

x

-direction

4

\sqrt{2} F

along negative

x

-direction

Explanation:

$F_{1} = F_{2}$ and angle between them is $120^{\circ}$

Electric Charges and Fields

267919 Three point charges $+ q, + q$ and $- q$ are placed at the corners of an equilateral triangle of side ' $a$ ' . Another charge $+ Q$ is kept at the centroid. Force exerted on $Q$ is:

1

\frac{1}{4 π ε_{0}} \frac{2 q Q}{a^{2}}

2

\frac{1}{4 π ε_{0}} \frac{6 q Q}{a^{2}}

3

\frac{1}{4 π ε_{0}} \frac{8 q Q}{a^{2}}

4

\frac{1}{4 π ε_{0}} \frac{14 q Q}{a^{2}}

Explanation:

$F = {(\frac{1}{4 π ε_{0}} \frac{q}{r^{2}})}^{2}$ where $r = \frac{a}{\sqrt{3}}$

Electric Charges and Fields

267920 Three charges $- q_{1}, + q_{2}$ and $- q_{3}$ are placed as shown in fig. The $X$ -component of the force on $- q_{1}$ is proportional to

1

\frac{q_{2}}{b^{2}} - \frac{q_{3}}{a^{2}} \cos θ

2

\frac{q_{2}}{b^{2}} + \frac{q_{3}}{a^{2}} \sin θ

3

\frac{q_{2}}{b^{2}} + \frac{q_{2}}{a^{2}} \cos θ

4 $\frac{q_2}{b^2}-\frac{q_2}{a^2} \sin \theta$

Electric Charges and Fields

272130 Three charges $+ q, + 2 q$ and $+ 4 q$ are connected by strings as shown in the figure. What is ratio of tensions in the strings $A B$ and $B C$ ?

1

1 : 2

2

1 : 3

3

2 : 1

4

3 : 1

Explanation:

(b) $T_{A B} = \frac{k q \cdot 2 q}{d^{2}} + \frac{k q \cdot 4 q}{{(2 d)}^{2}} = \frac{3 k q^{2}}{d}$
$T_{B C} = \frac{k \cdot 4 q \cdot 2 q}{d^{2}} + \frac{k q \cdot 4 q}{{(2 d)}^{2}} = \frac{9 k q^{2}}{d^{2}}$

NCERT Page-12 / N-7

Electric Charges and Fields

272131 The figure shows a charge $+ q$ at point $P$ held in equilibrium in air with the help of four $+ q$ charges situated at the vertices of a square: The net electrostatic force on $q$ is given by

1 Newton's

2 Coulomb's law

3 Principle of superposition

4 Net electric flux out the position of

+ q

.

Explanation:

(c) The weight $m g$ of the charge hold in air is in equillibrium with net electrostatic force exerted by the four charges situated at the corners. The net electrostatic force is given by the vector sum of the individual forces exerted by the charges at the corners. This is principle of superposition.

NCERT Page-15/ N-12