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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359418 The electrostatic potential on the surface of a charged conducting sphere is 50 $V$ . Two statements are made in this regard.
$S_{1}$ : At any point inside the sphere, electric intensity is zero.
$S_{2}$ : At any point inside the sphere, electrostatic potential is 50 $V$ .
Which of the following is a correct statement?

1

S_{1}

is true,

S_{2}

is also true and

S_{1}

is the cause of

S_{2}

2

S_{1}

is true but

S_{2}

is false.

3

S_{1}

is true

S_{2}

is also true but the statements are independent.

4 Both

S_{1}

and

S_{2}

are false.

Explanation:

We know that, at any point inside a charged conducting sphere, $E = 0$ and $E = - \frac{d V}{d r} = - \frac{d}{d r} (c o n s t a n t) = Z e r o$

NCERT Exemplar

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359419 Assertion :
Two concentric conducting spherical shells are charged. The charge on the outer shell is varied keeping the charge on inner shell constant, as a result the electric potential difference between the two shells does not change.
Reason :
In the situation of assertion, the electric field in the region between both the shells depends only on the charge existing on the inner shell.

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:

When the charge $Q_{1}$ on the inner shell is kept constant, changing the charge on the outer shell $(Q_{2})$ does not affect the electric potential difference between the two shells.
supporting img
The reason correctly explains this situation by noting that the electric field in the region between the shells depends only on the charge on the inner shell, which remains constant. So correct option is (1).

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359420 Assertion :
Electric potential of earth is taken zero.
Reason :
No electric field exist on earth surface.

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.

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359421 A system consists of two metallic spheres of radii $r_{1}$ and $r_{2}$ connected by a thin wire and a switch $S$ as shown. Initially S is open and spheres carry charges $q_{1}$ and $q_{2}$ respectively. If the switch is closed, the potential of the system is:
supporting img

1

(1 / 4 π ε_{o}) {q_{1} q_{2} / r_{1} r_{2}}

2

(1 / 4 π ε_{o}) {(q_{1} + q_{2}) / (r_{1} + r_{2})}

3

(1 / 4 π ε_{o}) {(q_{1} / r_{1}) / (q_{2} / r_{2})}

4

(1 / 4 π ε_{o}) {(q_{1} + q_{2}) / (r_{1} r_{2})^{1 / 2}}

Explanation:

Both the spheres form capacitance with infinity and both are said to be in parallel as shown in the figure.
supporting img
The total charge is $q_{1} + q_{2}$
Net capacitance is $C_{1} + C_{2}$
$V = \frac{q_{1} + q_{2}}{C_{1} + C_{2}} = \frac{q_{1} + q_{2}}{4 π ε_{o} (r_{1} + r_{2})}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359418 The electrostatic potential on the surface of a charged conducting sphere is 50 $V$ . Two statements are made in this regard.
$S_{1}$ : At any point inside the sphere, electric intensity is zero.
$S_{2}$ : At any point inside the sphere, electrostatic potential is 50 $V$ .
Which of the following is a correct statement?

1

S_{1}

is true,

S_{2}

is also true and

S_{1}

is the cause of

S_{2}

2

S_{1}

is true but

S_{2}

is false.

3

S_{1}

is true

S_{2}

is also true but the statements are independent.

4 Both

S_{1}

and

S_{2}

are false.

Explanation:

We know that, at any point inside a charged conducting sphere, $E = 0$ and $E = - \frac{d V}{d r} = - \frac{d}{d r} (c o n s t a n t) = Z e r o$

NCERT Exemplar

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359419 Assertion :
Two concentric conducting spherical shells are charged. The charge on the outer shell is varied keeping the charge on inner shell constant, as a result the electric potential difference between the two shells does not change.
Reason :
In the situation of assertion, the electric field in the region between both the shells depends only on the charge existing on the inner shell.

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:

When the charge $Q_{1}$ on the inner shell is kept constant, changing the charge on the outer shell $(Q_{2})$ does not affect the electric potential difference between the two shells.
supporting img
The reason correctly explains this situation by noting that the electric field in the region between the shells depends only on the charge on the inner shell, which remains constant. So correct option is (1).

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359420 Assertion :
Electric potential of earth is taken zero.
Reason :
No electric field exist on earth surface.

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.

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359421 A system consists of two metallic spheres of radii $r_{1}$ and $r_{2}$ connected by a thin wire and a switch $S$ as shown. Initially S is open and spheres carry charges $q_{1}$ and $q_{2}$ respectively. If the switch is closed, the potential of the system is:
supporting img

1

(1 / 4 π ε_{o}) {q_{1} q_{2} / r_{1} r_{2}}

2

(1 / 4 π ε_{o}) {(q_{1} + q_{2}) / (r_{1} + r_{2})}

3

(1 / 4 π ε_{o}) {(q_{1} / r_{1}) / (q_{2} / r_{2})}

4

(1 / 4 π ε_{o}) {(q_{1} + q_{2}) / (r_{1} r_{2})^{1 / 2}}

Explanation:

Both the spheres form capacitance with infinity and both are said to be in parallel as shown in the figure.
supporting img
The total charge is $q_{1} + q_{2}$
Net capacitance is $C_{1} + C_{2}$
$V = \frac{q_{1} + q_{2}}{C_{1} + C_{2}} = \frac{q_{1} + q_{2}}{4 π ε_{o} (r_{1} + r_{2})}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359418 The electrostatic potential on the surface of a charged conducting sphere is 50 $V$ . Two statements are made in this regard.
$S_{1}$ : At any point inside the sphere, electric intensity is zero.
$S_{2}$ : At any point inside the sphere, electrostatic potential is 50 $V$ .
Which of the following is a correct statement?

1

S_{1}

is true,

S_{2}

is also true and

S_{1}

is the cause of

S_{2}

2

S_{1}

is true but

S_{2}

is false.

3

S_{1}

is true

S_{2}

is also true but the statements are independent.

4 Both

S_{1}

and

S_{2}

are false.

Explanation:

We know that, at any point inside a charged conducting sphere, $E = 0$ and $E = - \frac{d V}{d r} = - \frac{d}{d r} (c o n s t a n t) = Z e r o$

NCERT Exemplar

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359419 Assertion :
Two concentric conducting spherical shells are charged. The charge on the outer shell is varied keeping the charge on inner shell constant, as a result the electric potential difference between the two shells does not change.
Reason :
In the situation of assertion, the electric field in the region between both the shells depends only on the charge existing on the inner shell.

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:

When the charge $Q_{1}$ on the inner shell is kept constant, changing the charge on the outer shell $(Q_{2})$ does not affect the electric potential difference between the two shells.
supporting img
The reason correctly explains this situation by noting that the electric field in the region between the shells depends only on the charge on the inner shell, which remains constant. So correct option is (1).

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359420 Assertion :
Electric potential of earth is taken zero.
Reason :
No electric field exist on earth surface.

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.

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359421 A system consists of two metallic spheres of radii $r_{1}$ and $r_{2}$ connected by a thin wire and a switch $S$ as shown. Initially S is open and spheres carry charges $q_{1}$ and $q_{2}$ respectively. If the switch is closed, the potential of the system is:
supporting img

1

(1 / 4 π ε_{o}) {q_{1} q_{2} / r_{1} r_{2}}

2

(1 / 4 π ε_{o}) {(q_{1} + q_{2}) / (r_{1} + r_{2})}

3

(1 / 4 π ε_{o}) {(q_{1} / r_{1}) / (q_{2} / r_{2})}

4

(1 / 4 π ε_{o}) {(q_{1} + q_{2}) / (r_{1} r_{2})^{1 / 2}}

Explanation:

Both the spheres form capacitance with infinity and both are said to be in parallel as shown in the figure.
supporting img
The total charge is $q_{1} + q_{2}$
Net capacitance is $C_{1} + C_{2}$
$V = \frac{q_{1} + q_{2}}{C_{1} + C_{2}} = \frac{q_{1} + q_{2}}{4 π ε_{o} (r_{1} + r_{2})}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359418 The electrostatic potential on the surface of a charged conducting sphere is 50 $V$ . Two statements are made in this regard.
$S_{1}$ : At any point inside the sphere, electric intensity is zero.
$S_{2}$ : At any point inside the sphere, electrostatic potential is 50 $V$ .
Which of the following is a correct statement?

1

S_{1}

is true,

S_{2}

is also true and

S_{1}

is the cause of

S_{2}

2

S_{1}

is true but

S_{2}

is false.

3

S_{1}

is true

S_{2}

is also true but the statements are independent.

4 Both

S_{1}

and

S_{2}

are false.

Explanation:

We know that, at any point inside a charged conducting sphere, $E = 0$ and $E = - \frac{d V}{d r} = - \frac{d}{d r} (c o n s t a n t) = Z e r o$

NCERT Exemplar

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359419 Assertion :
Two concentric conducting spherical shells are charged. The charge on the outer shell is varied keeping the charge on inner shell constant, as a result the electric potential difference between the two shells does not change.
Reason :
In the situation of assertion, the electric field in the region between both the shells depends only on the charge existing on the inner shell.

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:

When the charge $Q_{1}$ on the inner shell is kept constant, changing the charge on the outer shell $(Q_{2})$ does not affect the electric potential difference between the two shells.
supporting img
The reason correctly explains this situation by noting that the electric field in the region between the shells depends only on the charge on the inner shell, which remains constant. So correct option is (1).

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359420 Assertion :
Electric potential of earth is taken zero.
Reason :
No electric field exist on earth surface.

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.

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359421 A system consists of two metallic spheres of radii $r_{1}$ and $r_{2}$ connected by a thin wire and a switch $S$ as shown. Initially S is open and spheres carry charges $q_{1}$ and $q_{2}$ respectively. If the switch is closed, the potential of the system is:
supporting img

1

(1 / 4 π ε_{o}) {q_{1} q_{2} / r_{1} r_{2}}

2

(1 / 4 π ε_{o}) {(q_{1} + q_{2}) / (r_{1} + r_{2})}

3

(1 / 4 π ε_{o}) {(q_{1} / r_{1}) / (q_{2} / r_{2})}

4

(1 / 4 π ε_{o}) {(q_{1} + q_{2}) / (r_{1} r_{2})^{1 / 2}}

Explanation:

Both the spheres form capacitance with infinity and both are said to be in parallel as shown in the figure.
supporting img
The total charge is $q_{1} + q_{2}$
Net capacitance is $C_{1} + C_{2}$
$V = \frac{q_{1} + q_{2}}{C_{1} + C_{2}} = \frac{q_{1} + q_{2}}{4 π ε_{o} (r_{1} + r_{2})}$

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