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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359366 Potential at the centre due to charged arc is
supporting img

1

\frac{λ}{2 ε_{0}}

2

\frac{λ}{3 ε_{0}}

3

\frac{λ}{4 ε_{0}}

4

\frac{λ}{6 ε_{0}}

Explanation:

$V = \frac{k Q}{R} = \frac{1}{4 π ϵ_{0}} λ \times 2 π a \times \frac{120^{\circ}}{360^{\circ}}$
$= \frac{λ}{2 ε_{0}} \times \frac{1}{3} = \frac{λ}{6 ε_{0}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359367 A circular ring carries a uniformly distributed positive charge. The electric field ( $E$ ) and potential ( $V$ ) varies with distance ( $r$ ) from the centre of the ring along its axis as
supporting img

1

b

and

c

are true

2

a, b, c, d

are true

3

a

is true

4

a, b, c

are true

Explanation:

The electric field and potential on the axis of a circular charged ring is
$E = \frac{q x}{4 π ε_{0} {(R^{2} + x^{2})}^{3 / 2}}$
$V = \frac{q}{4 π ε_{0} \sqrt{R^{2} + x^{2}}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359368 An arc of radius $r$ carries charge. The linear density of charge is $λ$ and the arc subtends an angle $\frac{π}{3}$ at the centre. What is Electric potential at the centre?

1

\frac{λ}{4 ε_{0}}

2

\frac{λ}{8 ε_{0}}

3

\frac{λ}{12 ε_{0}}

4

\frac{λ}{16 ε_{0}}

Explanation:

Length of the arc $= r θ = \frac{r π}{3}$
Charge on the arc $= \frac{r π}{3} \times λ$
$∴$ Potential at centre $= \frac{k q}{r}$
$= \frac{1}{4 π ε_{0}} \times \frac{r π}{3} \frac{λ}{r} = \frac{λ r}{12 ε_{0}}$
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359369 The arrangement shown consists of three elements.
supporting img

(i) A thin rod of charge $- 3.0 μ C$ that forms a full circle of radius $6.0 c m$ .
(ii) A second thin rod charge $2.0 μ C$ that forms a circular arc of radius $4.0 c m$ and concentric with the full circle, subtending an angle of $90^{\circ}$ at the centre of the full circle.
(iii) An electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude $1.28 \times 10^{- 21} C$ - $m .$
The net electric potential in volts at the centre is

1 0

2 2

3 1

4 4

Explanation:

Potential due to dipole at the centre of the circle is zero.
Potentials due to charge on circle $= V_{1} = \frac{K \cdot (- 3 \times 10^{- 6})}{6 \times 10^{- 2}}$
Potential due to arc $V_{2} = \frac{K \cdot (2 \times 10^{- 6})}{4 \times 10^{- 2}}$
Net potential $= V_{1} + V_{2} = 0$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359370 Match the Column I and Column II
Column I
Column II
A
Electric potential near isolated positive charge
P
Negative
B
Electric potential near an isolated negative charge
Q
Positive
C
Electric potential due to a charge at its own location
R
Inversely of radius
D
Electric potential by a point charge varies
S
Infinite

1 A - Q, B - P, C - S, D - R

2 A - P, B - R, C - S, D - Q

3 A - S, B - P, C - R, D - S

4 A - R, B - Q, C - P, D - S

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359366 Potential at the centre due to charged arc is
supporting img

1

\frac{λ}{2 ε_{0}}

2

\frac{λ}{3 ε_{0}}

3

\frac{λ}{4 ε_{0}}

4

\frac{λ}{6 ε_{0}}

Explanation:

$V = \frac{k Q}{R} = \frac{1}{4 π ϵ_{0}} λ \times 2 π a \times \frac{120^{\circ}}{360^{\circ}}$
$= \frac{λ}{2 ε_{0}} \times \frac{1}{3} = \frac{λ}{6 ε_{0}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359367 A circular ring carries a uniformly distributed positive charge. The electric field ( $E$ ) and potential ( $V$ ) varies with distance ( $r$ ) from the centre of the ring along its axis as
supporting img

1

b

and

c

are true

2

a, b, c, d

are true

3

a

is true

4

a, b, c

are true

Explanation:

The electric field and potential on the axis of a circular charged ring is
$E = \frac{q x}{4 π ε_{0} {(R^{2} + x^{2})}^{3 / 2}}$
$V = \frac{q}{4 π ε_{0} \sqrt{R^{2} + x^{2}}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359368 An arc of radius $r$ carries charge. The linear density of charge is $λ$ and the arc subtends an angle $\frac{π}{3}$ at the centre. What is Electric potential at the centre?

1

\frac{λ}{4 ε_{0}}

2

\frac{λ}{8 ε_{0}}

3

\frac{λ}{12 ε_{0}}

4

\frac{λ}{16 ε_{0}}

Explanation:

Length of the arc $= r θ = \frac{r π}{3}$
Charge on the arc $= \frac{r π}{3} \times λ$
$∴$ Potential at centre $= \frac{k q}{r}$
$= \frac{1}{4 π ε_{0}} \times \frac{r π}{3} \frac{λ}{r} = \frac{λ r}{12 ε_{0}}$
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359369 The arrangement shown consists of three elements.
supporting img

(i) A thin rod of charge $- 3.0 μ C$ that forms a full circle of radius $6.0 c m$ .
(ii) A second thin rod charge $2.0 μ C$ that forms a circular arc of radius $4.0 c m$ and concentric with the full circle, subtending an angle of $90^{\circ}$ at the centre of the full circle.
(iii) An electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude $1.28 \times 10^{- 21} C$ - $m .$
The net electric potential in volts at the centre is

1 0

2 2

3 1

4 4

Explanation:

Potential due to dipole at the centre of the circle is zero.
Potentials due to charge on circle $= V_{1} = \frac{K \cdot (- 3 \times 10^{- 6})}{6 \times 10^{- 2}}$
Potential due to arc $V_{2} = \frac{K \cdot (2 \times 10^{- 6})}{4 \times 10^{- 2}}$
Net potential $= V_{1} + V_{2} = 0$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359370 Match the Column I and Column II
Column I
Column II
A
Electric potential near isolated positive charge
P
Negative
B
Electric potential near an isolated negative charge
Q
Positive
C
Electric potential due to a charge at its own location
R
Inversely of radius
D
Electric potential by a point charge varies
S
Infinite

1 A - Q, B - P, C - S, D - R

2 A - P, B - R, C - S, D - Q

3 A - S, B - P, C - R, D - S

4 A - R, B - Q, C - P, D - S

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359366 Potential at the centre due to charged arc is
supporting img

1

\frac{λ}{2 ε_{0}}

2

\frac{λ}{3 ε_{0}}

3

\frac{λ}{4 ε_{0}}

4

\frac{λ}{6 ε_{0}}

Explanation:

$V = \frac{k Q}{R} = \frac{1}{4 π ϵ_{0}} λ \times 2 π a \times \frac{120^{\circ}}{360^{\circ}}$
$= \frac{λ}{2 ε_{0}} \times \frac{1}{3} = \frac{λ}{6 ε_{0}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359367 A circular ring carries a uniformly distributed positive charge. The electric field ( $E$ ) and potential ( $V$ ) varies with distance ( $r$ ) from the centre of the ring along its axis as
supporting img

1

b

and

c

are true

2

a, b, c, d

are true

3

a

is true

4

a, b, c

are true

Explanation:

The electric field and potential on the axis of a circular charged ring is
$E = \frac{q x}{4 π ε_{0} {(R^{2} + x^{2})}^{3 / 2}}$
$V = \frac{q}{4 π ε_{0} \sqrt{R^{2} + x^{2}}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359368 An arc of radius $r$ carries charge. The linear density of charge is $λ$ and the arc subtends an angle $\frac{π}{3}$ at the centre. What is Electric potential at the centre?

1

\frac{λ}{4 ε_{0}}

2

\frac{λ}{8 ε_{0}}

3

\frac{λ}{12 ε_{0}}

4

\frac{λ}{16 ε_{0}}

Explanation:

Length of the arc $= r θ = \frac{r π}{3}$
Charge on the arc $= \frac{r π}{3} \times λ$
$∴$ Potential at centre $= \frac{k q}{r}$
$= \frac{1}{4 π ε_{0}} \times \frac{r π}{3} \frac{λ}{r} = \frac{λ r}{12 ε_{0}}$
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359369 The arrangement shown consists of three elements.
supporting img

(i) A thin rod of charge $- 3.0 μ C$ that forms a full circle of radius $6.0 c m$ .
(ii) A second thin rod charge $2.0 μ C$ that forms a circular arc of radius $4.0 c m$ and concentric with the full circle, subtending an angle of $90^{\circ}$ at the centre of the full circle.
(iii) An electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude $1.28 \times 10^{- 21} C$ - $m .$
The net electric potential in volts at the centre is

1 0

2 2

3 1

4 4

Explanation:

Potential due to dipole at the centre of the circle is zero.
Potentials due to charge on circle $= V_{1} = \frac{K \cdot (- 3 \times 10^{- 6})}{6 \times 10^{- 2}}$
Potential due to arc $V_{2} = \frac{K \cdot (2 \times 10^{- 6})}{4 \times 10^{- 2}}$
Net potential $= V_{1} + V_{2} = 0$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359370 Match the Column I and Column II
Column I
Column II
A
Electric potential near isolated positive charge
P
Negative
B
Electric potential near an isolated negative charge
Q
Positive
C
Electric potential due to a charge at its own location
R
Inversely of radius
D
Electric potential by a point charge varies
S
Infinite

1 A - Q, B - P, C - S, D - R

2 A - P, B - R, C - S, D - Q

3 A - S, B - P, C - R, D - S

4 A - R, B - Q, C - P, D - S

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359366 Potential at the centre due to charged arc is
supporting img

1

\frac{λ}{2 ε_{0}}

2

\frac{λ}{3 ε_{0}}

3

\frac{λ}{4 ε_{0}}

4

\frac{λ}{6 ε_{0}}

Explanation:

$V = \frac{k Q}{R} = \frac{1}{4 π ϵ_{0}} λ \times 2 π a \times \frac{120^{\circ}}{360^{\circ}}$
$= \frac{λ}{2 ε_{0}} \times \frac{1}{3} = \frac{λ}{6 ε_{0}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359367 A circular ring carries a uniformly distributed positive charge. The electric field ( $E$ ) and potential ( $V$ ) varies with distance ( $r$ ) from the centre of the ring along its axis as
supporting img

1

b

and

c

are true

2

a, b, c, d

are true

3

a

is true

4

a, b, c

are true

Explanation:

The electric field and potential on the axis of a circular charged ring is
$E = \frac{q x}{4 π ε_{0} {(R^{2} + x^{2})}^{3 / 2}}$
$V = \frac{q}{4 π ε_{0} \sqrt{R^{2} + x^{2}}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359368 An arc of radius $r$ carries charge. The linear density of charge is $λ$ and the arc subtends an angle $\frac{π}{3}$ at the centre. What is Electric potential at the centre?

1

\frac{λ}{4 ε_{0}}

2

\frac{λ}{8 ε_{0}}

3

\frac{λ}{12 ε_{0}}

4

\frac{λ}{16 ε_{0}}

Explanation:

Length of the arc $= r θ = \frac{r π}{3}$
Charge on the arc $= \frac{r π}{3} \times λ$
$∴$ Potential at centre $= \frac{k q}{r}$
$= \frac{1}{4 π ε_{0}} \times \frac{r π}{3} \frac{λ}{r} = \frac{λ r}{12 ε_{0}}$
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359369 The arrangement shown consists of three elements.
supporting img

(i) A thin rod of charge $- 3.0 μ C$ that forms a full circle of radius $6.0 c m$ .
(ii) A second thin rod charge $2.0 μ C$ that forms a circular arc of radius $4.0 c m$ and concentric with the full circle, subtending an angle of $90^{\circ}$ at the centre of the full circle.
(iii) An electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude $1.28 \times 10^{- 21} C$ - $m .$
The net electric potential in volts at the centre is

1 0

2 2

3 1

4 4

Explanation:

Potential due to dipole at the centre of the circle is zero.
Potentials due to charge on circle $= V_{1} = \frac{K \cdot (- 3 \times 10^{- 6})}{6 \times 10^{- 2}}$
Potential due to arc $V_{2} = \frac{K \cdot (2 \times 10^{- 6})}{4 \times 10^{- 2}}$
Net potential $= V_{1} + V_{2} = 0$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359370 Match the Column I and Column II
Column I
Column II
A
Electric potential near isolated positive charge
P
Negative
B
Electric potential near an isolated negative charge
Q
Positive
C
Electric potential due to a charge at its own location
R
Inversely of radius
D
Electric potential by a point charge varies
S
Infinite

1 A - Q, B - P, C - S, D - R

2 A - P, B - R, C - S, D - Q

3 A - S, B - P, C - R, D - S

4 A - R, B - Q, C - P, D - S

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359366 Potential at the centre due to charged arc is
supporting img

1

\frac{λ}{2 ε_{0}}

2

\frac{λ}{3 ε_{0}}

3

\frac{λ}{4 ε_{0}}

4

\frac{λ}{6 ε_{0}}

Explanation:

$V = \frac{k Q}{R} = \frac{1}{4 π ϵ_{0}} λ \times 2 π a \times \frac{120^{\circ}}{360^{\circ}}$
$= \frac{λ}{2 ε_{0}} \times \frac{1}{3} = \frac{λ}{6 ε_{0}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359367 A circular ring carries a uniformly distributed positive charge. The electric field ( $E$ ) and potential ( $V$ ) varies with distance ( $r$ ) from the centre of the ring along its axis as
supporting img

1

b

and

c

are true

2

a, b, c, d

are true

3

a

is true

4

a, b, c

are true

Explanation:

The electric field and potential on the axis of a circular charged ring is
$E = \frac{q x}{4 π ε_{0} {(R^{2} + x^{2})}^{3 / 2}}$
$V = \frac{q}{4 π ε_{0} \sqrt{R^{2} + x^{2}}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359368 An arc of radius $r$ carries charge. The linear density of charge is $λ$ and the arc subtends an angle $\frac{π}{3}$ at the centre. What is Electric potential at the centre?

1

\frac{λ}{4 ε_{0}}

2

\frac{λ}{8 ε_{0}}

3

\frac{λ}{12 ε_{0}}

4

\frac{λ}{16 ε_{0}}

Explanation:

Length of the arc $= r θ = \frac{r π}{3}$
Charge on the arc $= \frac{r π}{3} \times λ$
$∴$ Potential at centre $= \frac{k q}{r}$
$= \frac{1}{4 π ε_{0}} \times \frac{r π}{3} \frac{λ}{r} = \frac{λ r}{12 ε_{0}}$
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359369 The arrangement shown consists of three elements.
supporting img

(i) A thin rod of charge $- 3.0 μ C$ that forms a full circle of radius $6.0 c m$ .
(ii) A second thin rod charge $2.0 μ C$ that forms a circular arc of radius $4.0 c m$ and concentric with the full circle, subtending an angle of $90^{\circ}$ at the centre of the full circle.
(iii) An electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude $1.28 \times 10^{- 21} C$ - $m .$
The net electric potential in volts at the centre is

1 0

2 2

3 1

4 4

Explanation:

Potential due to dipole at the centre of the circle is zero.
Potentials due to charge on circle $= V_{1} = \frac{K \cdot (- 3 \times 10^{- 6})}{6 \times 10^{- 2}}$
Potential due to arc $V_{2} = \frac{K \cdot (2 \times 10^{- 6})}{4 \times 10^{- 2}}$
Net potential $= V_{1} + V_{2} = 0$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359370 Match the Column I and Column II
Column I
Column II
A
Electric potential near isolated positive charge
P
Negative
B
Electric potential near an isolated negative charge
Q
Positive
C
Electric potential due to a charge at its own location
R
Inversely of radius
D
Electric potential by a point charge varies
S
Infinite

1 A - Q, B - P, C - S, D - R

2 A - P, B - R, C - S, D - Q

3 A - S, B - P, C - R, D - S

4 A - R, B - Q, C - P, D - S