Download electric field and charges

Electric Charge And Field
1 Mark
1. Define dipole moment of an electric dipole. Is it a scalar or a vector?
Electric dipole moment of an electric dipole is equal to the product of either charge
and distance between the two charges. It is a vector quantity.
2. Why must electrostatic field be normal to the surface at every point of a charged
conduction?
The component of electric field along the tangent to the surface of the conductor
must be zero 𝑬 𝐜𝐨𝐬 𝜽 = 𝟎 where θ is angle between and tangent to the surface.
As E≠ 𝟎 or θ = 900 Hence E is perpendicular to the surface
3. A proton is placed in a uniform electric field directed along the position x-axis. In which
direction will it tend to move?
Proton will tend to move along X axis in the direction of electric field.
4. Why do the electric field lines not form closed loop?
No electric field exist from negative to p[ositive charge , hence electric field lines do
not form closed loop.
5. In which orientation a dipole placed in a uniform electric field is in a) Stable, b) Unstable
Equilibrium?
(a) For stable equilibrium the angle between p and E must be 00
(b) For unstable equilibrium the angle between p and E must be 1800
2 Marks
1. Charges of magnitudes 2Q and –Q are located at points (a, 0, 0) and (4a, 0, 0). Find the
ratio of the flux of electric field due to these charges through concentric sphere as of radii
2a and 8a centered at the origin.
2.
Ans:
ф1
ф2
2𝑄
= 2𝑄−𝑄 =
2
1
2. Two Charges of magnitudes -3Q and +2Q are located at points (a, 0) and (4a, 0)
respectively. What is the electric flux due to these charges through a sphere of radius 5a
with the centre at the origin?
2.
Ans:
ΦE =
−3𝑄+2𝑄
∈0
=
𝑄
∈0
.
3. Two concentric spherical shell of radii R and 2R are given charges Q1 and Q2respectively.
The surface charge densities on outer surface are equal. Determine the ratio of charges Q1
and Q2.
2.
Ans:
𝑄1
𝑄2
=
4𝜋𝑅2
4𝜋(2𝑅)2
=
1
4
4. Define electric field intensity. Write its SI unit. Is it scalar or vector?
2.
Ans:
Electric field intensity E can be defined as the force experienced per unit charge at
that point. Its SI unit is N/C. It is a vector quantity. E =
𝑭
𝒒
5. Force of attraction between two point charges placed at a distance d is F. What distance
apart should they be kept in the same medium so that the force between them is F/3?
2.
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Ans:
𝐹′
𝐹
=
𝑑2
𝑑21
or
𝐹
3𝐹
=
𝑑2
∴ d1 = √3 d
𝑑21
𝟏
6. Plot a graph showing the variation of Coulomb’s force F versus 𝟐 , where r is the distance
𝒓
between the two charges (1µC, 2µC) and (2µC -3µC) . Interpret the graphs obtained.
Ans:
Coulomb’s force between two charges q1 and q2 separated by a distance r is given by
1
F 𝛼 q1.q2 and F 𝛼 𝑟2 . F is repulsive between like charges (1µC, 2µC) and F is attractive
between unlike charges ((2µC, -3µC)
Attractive
1
𝑟2
Repulsive
7. An electric dipole moment 4 x 10-9 cm is aligned at 300 with the direction of a uniform
electric field of magnitude 5 x 104 N/C. Calculate the magnitude of the torque acting on the
dipole.
Ans:
1
𝜏 = PE sin𝜃 = 4 x 10-9 x 5 x 104 x sin300 = 4 x 10-9 x 5 x 104 x = 1 x 10-4 Nm.
2
8. Two fixed point charges +4e and +e units are separated by a distance a. Where a third
charge q should be placed for it to be in equilibrium?
+4e ----------- x -------------------(a-x)-------- e
1
4𝑒 𝑥 𝑞
4𝜋𝜖0
𝑥2
=
1
𝑒𝑥𝑞
4𝜋𝜖0 (𝑎−𝑥)2
or 4(a-x)2 = x2 or 2(a-x) = x ∴x =
2𝑎
3
3 Marks
1. a) A point charge (+Q) is kept in the vicinity of uncharged conducting plate. Sketch electric
fieldlines between the charge and the plate.
(b) Two infinitely large plane thin parallel sheets having surface charge densities σ1 and
σ2(σ1 > σ2 ) are shown in the figure. Write the magnitudes and directions of the net fields in
theregions marked II and III.
(a) The lines of force start from + Q and terminate at metal place inducing negative charge
on it. The lines of force will be perpendicular to the metal surface.
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(b) (i) Net electric field in region II
𝟏
𝟐
𝑬 = (𝝈𝟏− 𝝈𝟐 ) Direction of electric field in from sheet A to sheet B.
(ii) Net electric field in region III
𝟏
𝟐
𝑬 = (𝝈𝟏+ 𝝈𝟐 )Direction is away from the two sheets i.e. towards right side.
2. Given a uniform electric field E = 5 × 103i N/C, find the flux of this field through a square of
10 cm on a side whose plane is parallel to the y-z plane. What would be the flux through the
same square if the plane makes a 30° angle with the x-axis?
3. Deduce the expression for the torque acting on a dipole of dipole moment p in the presence
of a uniform electric field E .
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4. (a)A point charge +10 μC is a distance 5 cm directly above the centre of a
square of side 10 cm, as shown in Fig. What is the magnitude of the electric
flux through the square?
(b) If area of this square is reduced to half, what will be the new electric flux?
Ans:
5.
Write any three properties of electric lines of force.
Ans: (i) They originate from positive and terminate at negative charge.
(ii) Electric field lines never intersect each other.
(iii) Electric field lines of similar charges exert lateral pressure.
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5 Marks
1. Derive expression for electric field at a point on the axial line of the dipole. Give the direction
of electric field at the point.
Ans: The axial line of a dipole is the line passing through the positive and negative
charges of the electric dipole.
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2. An electric dipole is held in uniform electric field
(i) Show that no translator force acts on it.
(ii) Derive an expression for the torque acting on it.
Ans:
3.
State Gauss Theorem. A thin charged wire of infinite length has line charge density ‘λ’.
Derive expression for electric field at a distance ‘r’.
Ans:
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4. Charge q is distributed uniformly on a spherical shell of radius R. Using gauss law
derive expression of electric field at a distance r from the centre when (i)r>R (ii) r=R
(iii) r<R
Ans: Consider a hollow conducting sphere of radius R with its centre at O. let σ be its
surface density. The field at any point P, outside or inside depends upon the
distance from the centre of the spherical shell. Let the distance between the
centre of the spherical shell and the point be r.
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