Electric Charges and Fields Test

Result

Electric Charges and Fields Test - 9

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

Two parallel infinite line charges + λ and -λ are placed with a separation distance R in free space. Then etelectric field exactly mid - way between the two line charges is

A
zero

B
2λ/πε₀R

C
λ/πε₀R

D
λ/2πε₀R

Solution

Electric field at point P due to line charge distribution +λ,
E_+λ = away from +λ

Electric field at point P due to line charge distribution -λ,

E_+λ and E_-λ have same direction,
Question 2
4 / -1

An electric dipole consists of charges ±2.0 x 10^-8C separated by a distance of 2.0 x 10^-3 m. It is placed near a long line charge of linear charge density 4.0 x 10^-4C m^-1 as shown in the figure, such that the negative charge is at a distance of 2.0 cm from the line charge. The force acting on the dipole will be

A
7.2 N towards the line charge

B
6.6 N away from the line charge

C
0.6 N away from the line charge

D
0.6 N towards the line charge

Solution

The electric field at a distance r from the line charge of linear density λ is given by
E = λ/2πε₀r
Hence, the field at the negative charge,
E₁=
The force on the negative charge, F₁ = (3.6 x 10⁸) (2.0 x 10^-8) = 7.2 N towards the line charge
Similarly, the field at the positive charge,
i.e., at r = 0.022 m is E₂= 3.3 x10⁸ N ^-1
The force on the positive charge,
F₂ = (3.3 x 10⁸) x (2.0 x 10^-8) = 6.6 N away from the line charge.
Hence, the net force on the dipole = 7.2N - 6.6N = 0.6 N towards the line charge.
Question 3
4 / -1

Two infinite plane parallel sheets, separated by a distance d have equal and opposite uniform charge desities σ. Electric field at a point between the sheets is

A
σ/2ε₀

B
σ/ε₀

C
zero

D
depends on the location of the point

Solution

Electric field, E = σ/ε₀
Question 4
4 / -1

Two large, thin metal places are parallel and close to each other. On their faces, the plates have surface charge densities of opposite signs and of magnitude 16 x 10^-22 C m^-2. The electric field between the plates is

A
1.8 x 10^-10 N C^-1

B
1.9 x 10^-10 N C^-1

C
1.6 x 10^-10 N C^-1

D
1.5 x 10^-10 N C^-1

Solution

Here
Question 5
4 / -1

Two large thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and magnitude 27 x 10^-22C m^-2. The electric field in region II in between the plates is

A
4.25 x 10^-8N C^-1

B
6.28 x 10^-10N C^-1

C
3.05 x 10^-10N C^-1

D
5.03 x 10^-10N C^-1

Solution

The value of in the region II, in between the plates = 3.05 x 10^-10N C^-1
Question 6
4 / -1

A charged ball B hangs from a silk thread S, which makes an angle θ with a large charged conducting sheet P as shown in the figure. The surface charge density of the sheet is proportional to

A
cos θ

B
cot θ

C
sin θ

D
tan θ

Solution

T sinθ = σq/ε₀
T cosθ = mg
∴ tanθ = σq/ε₀mg
∴ σ is proportional to tanθ.
Question 7
4 / -1

Consider a thin spherical shell of radius R consisting of uniform surface charge density σ. The electric field at a point of distance x from its centre and outside the shell is

A
inversely proportional to σ

B
directly proportional to x²

C
directly proportional to R

D
inversely proportional to x²

Solution

For a thin uniformly charged spherical shell, the field points outside the shell at a distance x from the centre is

If the radius of the sphere is R, Q = σ4πR²

This is inversely proportional to square of the distance from the centre. It is as if the whole charge is concentrated at the centre.
Question 8
4 / -1

A non conducting sphere of radius a has a net charge +q uniformly distributed throughout its volume. A spherical conducting shell having inner and outer radii b and c and net charge −q is concentric with the sphere (see the figure).

Read the following statements

(i) The electric field at a distance r from the center of the sphere for r<a is

(ii) The electric field at distance r for A<r<b is 0
(iii) The electric field at distance r for b<r<c is 0
(iv) The charge on the inner surface of the spherical shell is −q
(v) The charge on the outer surface of the spherical shell is +q
Which of the above statements are true?

A
(i), (ii) and (v)

B
(i), (iii) and (iv)

C
(i), (ii) and (iv)

D
(ii), (iii) and (v)
Question 9
4 / -1

There is a solid sphere of radius R having uniformly distributed charge throughout it. What is the relation between electric field E and distance r from the centre (r < R)?

A
E ∝ r^-2

B
E ∝ r^-1

C
E ∝ r

D
E ∝ r²
Question 10
4 / -1

An early model for an atom considered it to have a positively charged point nucleus of charge Ze, surrounded by a uniform density of negative charge upto a radius R. The atom as a whole is neutral. The electric field at a distance r from the nucleus is (r < R).

A

B

C

D

Solution

Charge on nucleus is =+Ze
total negative charge =−Ze(∵ atoms is electrical neutral)
Negative charge density, ρ= charge/volume =

Consider a Gaussian surface with radius r
By Gauss's theorem

Charge enclosed by Gaussian surface
Using (i)
From (ii),