An oil drop of 12 excess electrons is held stationary under a constant electric field of 2 . 55 × 10 4 N / C (Millikan’s oil drop experiment). The density of the oil is 1 . 26 gm cm 3 . Estimate the radius of the drop. ( g = 9 . 8 m / s 2 ; e = 1 . 6 × 10 - 19 C ).

Given, Excess electrons on an oil drop, n = 12 Electric field intensity, E = 2.55 × 10 4 N C - 1 Density of oil, ρ = 1 .26 gm / cm 3 = 1 .26 × 10 3 kg/m 3 Acceleration due to gravity, g = 9.8 m s - 2 Charge on an electron, e = 1.6 × 10 - 19 C The total charge of the drop then becomes, q = n e = 12 × 1 . 6 × 10 - 19 C = 19 . 2 × 10 - 19 C Say, the radius of the sphere is r . The volume of the sphere then becomes, v = 4 3 π r 3 The mass of the sphere becomes, m = v ρ = 4 3 π r 3 ρ As the charge is held stationary under the electric field, the net force on a drop must be zero. Therefore, the force due to the electric field must be equal to the force due to gravity. ⇒ q E = m g ⇒ q E = 4 3 π r 3 ρ r = 3 E q 4 π ρ g 3 = 3 × 2.55 × 10 4 × 19 . 2 × 10 - 19 4 × 3.14 × 1.26 × 10 3 × 9.8 3 = 946.09 × 10 - 21 3 = 9.82 × 10 - 7 m

An oil drop of 12 excess electrons is held stationary under a constant electric field of 2 . 55 × 10 4 N / C (Millikan’s oil drop experiment). The density of the oil is 1 . 26 gm cm 3 . Estimate the radius of the drop. ( g = 9 . 8 m / s 2 ; e = 1 . 6 × 10 - 19 C ).

Given, Excess electrons on an oil drop, n = 12 Electric field intensity, E = 2.55 × 10 4 N C - 1 Density of oil, ρ = 1 .26 gm / cm 3 = 1 .26 × 10 3 kg/m 3 Acceleration due to gravity, g = 9.8 m s - 2 Charge on an electron, e = 1.6 × 10 - 19 C The total charge of the drop then becomes, q = n e = 12 × 1 . 6 × 10 - 19 C = 19 . 2 × 10 - 19 C Say, the radius of the sphere is r . The volume of the sphere then becomes, v = 4 3 π r 3 The mass of the sphere becomes, m = v ρ = 4 3 π r 3 ρ As the charge is held stationary under the electric field, the net force on a drop must be zero. Therefore, the force due to the electric field must be equal to the force due to gravity. ⇒ q E = m g ⇒ q E = 4 3 π r 3 ρ r = 3 E q 4 π ρ g 3 = 3 × 2.55 × 10 4 × 19 . 2 × 10 - 19 4 × 3.14 × 1.26 × 10 3 × 9.8 3 = 946.09 × 10 - 21 3 = 9.82 × 10 - 7 m

A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is ( σ / 2 ϵ 0 ) n ^ , where n ^ is the unit vector in the outward normal direction, and σ is the surface charge density near the hole.

Consider a shell with a hole with a charge density of σ . Say, the field due to the shell at the hole is E s as shown in the figure. Consider a small patch of same size as that of the hole with a charge density σ . Say, the field due to the patch is E h as shown. Assuming the patch to be a thin sheet, its field can be written as, E h = σ 2 ε 0 Combine the shell and the patch as shown in the figure to form a closed shell as shown in the figure. The field inside the shell becomes, E i n = E h - E s . We know that the field inside a conducting shell is zero. Therefore, E i n = 0 ⇒ E h - E s = 0 ⇒ E s = E h = σ 2 ε 0 Therefore, the vector representation of field due to the shell at the hole is, E s → = σ 2 ε 0 n ^

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An oil drop of $12$ excess electrons is held stationary under a constant electric field of $2.55 \times 10^{4} N / C$ (Millikan’s oil drop experiment). The density of the oil is $1.26 \frac{gm}{{cm}^{3}}$ . Estimate the radius of the drop. ( $g = 9.8 m / s^{2}$ ; $e = 1.6 \times 10^{- 19} C$ ).

Important Questions on Electric Charges and Fields

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>ADDITIONAL EXERCISES>Q 1.26

Which among the curves shown in the figure cannot possibly represent electrostatic field lines?

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>ADDITIONAL EXERCISES>Q 1.27

In a certain region of space, electric field is along the

z

-direction throughout. The magnitude of the electric field is, however, not constant but increases uniformly along the positive

z

-direction, at the rate of

10^{5} N / C

per meter. What are the force and torque experienced by a system having a total dipole moment equal to

10^{- 7} Cm

in the negative $z$ -direction?

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>ADDITIONAL EXERCISES>Q 1.28

A conductor $A$ with a cavity as shown in figure is given a charge $Q$ . Show that the entire charge must appear on the outer surface of the conductor.

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>ADDITIONAL EXERCISES>Q 1.28

A conductor $A$ with cavity as shown in the figure is given a charge $Q$ . Another conductor $B$ with charge $q$ is inserted into the cavity keeping $B$ insulated from $A$ . Show that the total charge on outside the surface of $A$ is $Q + q$ .

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>ADDITIONAL EXERCISES>Q 1.28

A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>ADDITIONAL EXERCISES>Q 1.29

A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is (

σ / 2 ϵ_{0}

)

\hat{n}

, where

\hat{n}

is the unit vector in the outward normal direction, and

σ

is the surface charge density near the hole.

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>ADDITIONAL EXERCISES>Q 1.3

Obtain the formula for the electric field due to a long thin wire of uniform linear charge density

E

without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary integral.]

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>ADDITIONAL EXERCISES>Q 1.31

It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted by

u

) of charge

+ (2 / 3) e,

and the ‘down’ quark (denoted by

d

) of charge

(- 1 / 3) e,

together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.

An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55×104 N/C (Millikan’s oil drop experiment). The density of the oil is 1.26 gmcm3. Estimate the radius of the drop. (g = 9.8 m/s2; e= 1.6×10-19C).

Important Questions on Electric Charges and Fields

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An oil drop of $12$ excess electrons is held stationary under a constant electric field of $2.55 \times 10^{4} N / C$ (Millikan’s oil drop experiment). The density of the oil is $1.26 \frac{gm}{{cm}^{3}}$ . Estimate the radius of the drop. ( $g = 9.8 m / s^{2}$ ; $e = 1.6 \times 10^{- 19} C$ ).