A slab of material of dielectric constant k has the same area as the plates of a parallel plate capacitor but has a thickness 3 d 4 . Find the ratio of the capacitance with dielectric inside it to its capacitance without the dielectric.

If V 0 is the potential difference when there is no dielectric, then the electric field between the capacitor plates will be E 0 = V 0 d After the dielectric is inserted, the electric field in the dielectric reduces to E = E 0 k Now the potential difference between the plates will be V = E 0 . d 4 + E . 3 d 4 = E 0 . d 4 + E 0 k . 3 d 4 = E 0 d 1 4 + 3 4 k = V 0 k + 3 4 k Thus the potential difference decreases by a factor of k + 3 4 k , while the free charge q 0 on the plates remains the same. The capacitance increases to a new value given by C = q 0 V = 4 k k + 3 . q 0 V 0 = 4 k k + 3 C 0 C C 0 = 4 k k + 3

EASY

12th CBSE

IMPORTANT

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Explain why, for any charge configuration, the equipotential surface through a point is normal to the electric field at that point.

Draw a sketch of equipotential surfaces due to a single charge $(- q)$ , depicting the electric field lines due to the charge.

Important Questions on Electrostatic Potential and Capacitance

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12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 5

Obtain an expression for the work done to dissociate the system of three charges placed at the vertices of an equilateral triangle of side $‘ a ’$ as shown here.

Question Image

MEDIUM

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 6

Define the capacitance of a capacitor. Obtain the expression for the capacitance of a parallel plate capacitor in the vacuum in terms of plate area

A

and separation

d

between the plates.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 6

A slab of material of dielectric constant

k

has the same area as the plates of a parallel plate capacitor but has a thickness

\frac{3 d}{4}

. Find the ratio of the capacitance with dielectric inside it to its capacitance without the dielectric.

MEDIUM

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 7

Distinguish, with the help of a suitable diagram, the difference in the behaviour of a conductor and a dielectric placed in an external electric field. How does a polarized dielectric modify the original external field?

MEDIUM

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 7

If two similar large plates, each of area

A

having surface charge densities

+ σ

and

- σ

are separated by a distance

d

in air, find the expressions for the field at points between the two plates and on the outer side of the plates. Specify the direction of the field in each case.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 7

If two similar large plates, each of area

A

having surface charge densities

+ σ

and

- σ

are separated by a distance

d

in air, find the expressions for the potential difference between the plates.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 7

If two similar large plates, each of area

A

having surface charge densities

+ σ

and

- σ

are separated by a distance

d

in air, find the expressions for the capacitance of the capacitor so formed.

MEDIUM

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 8

Obtain the expression for the capacitance of a parallel plate capacitor. Three capacitors of capacitances

C_{1}, C_{2}

and

C_{3}

are connected in series. Show that the energy stored in the series combination is the same as that in the parallel combination.

Explain why, for any charge configuration, the equipotential surface through a point is normal to the electric field at that point. Draw a sketch of equipotential surfaces due to a single charge -q, depicting the electric field lines due to the charge.

Important Questions on Electrostatic Potential and Capacitance

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Explain why, for any charge configuration, the equipotential surface through a point is normal to the electric field at that point.

Draw a sketch of equipotential surfaces due to a single charge $(- q)$ , depicting the electric field lines due to the charge.