Electric Charges and Fields Easy Questions and Answers | Page - 2

Electric Charges and Fields

The electric field at a distance 3R from the centre of a charged conducting spherical shell of
2

radius R is E. The electric field at a distance R from the centre of the sphere is
2

1. E
  2
1. zero
1. E
1. E
  2

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Electric field at a point inside a charged conducting spherical shell is zero.

Correct Option: B

Electric field at a point inside a charged conducting spherical shell is zero.

The electric potential V at any point (x, y, z), all in meters in space is given by V = 4x² volt. The electric field at the point (1, 0, 2) in volt/meter is

1. 8 along positive X-axis
1. 16 along negative X-axis
1. 16 along positive X-axis
1. 8 along negative X-axis

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E^{^→} = - dv î + dv ĵ + dv k̂
dx dy dz

= -8 × î volt/meter
∴ E^{^→} = -8î V / m

Correct Option: D

E^{^→} = - dv î + dv ĵ + dv k̂
dx dy dz

= -8 × î volt/meter
∴ E^{^→} = -8î V / m

An electric dipole of moment ´p´ is placed in an electric field of intensity ´E´. The dipole acquires a position such that the axis of the dipole makes an angle θ with the direction of the field. Assuming that the potential energy of the dipole to be zero when = 90°, the torque and the potential energy of the dipole will respectively be :

1. p E sin θ, – p E cos θ
1. p E sin θ, –2 p E cos θ
1. p E sin θ, 2 p E cos θ
1. p E cos θ, – p E cos θ

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The torque on the dipole is given as
τ = pE sin θ
The potential energy of the dipole in the electric field is given as
U = – pE cos θ

Correct Option: A

The torque on the dipole is given as
τ = pE sin θ
The potential energy of the dipole in the electric field is given as
U = – pE cos θ

An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90° is

1. pE²
1. p²E
1. pE
1. infinity

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When electric dipole is aligned parallel θ = 0° and the dipole is rotated by 90° i.e., θ = 90°.
Energy required to rotate the dipole W = U_f – U_i = (–pE cos 90°) – (–pE cos 0°)
= pE.

Correct Option: C

When electric dipole is aligned parallel θ = 0° and the dipole is rotated by 90° i.e., θ = 90°.
Energy required to rotate the dipole W = U_f – U_i = (–pE cos 90°) – (–pE cos 0°)
= pE.

Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (d << l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as :

1. v ∝ x^{1 / 2}
1. v ∝ x
1. v ∝ x^{-1 / 2}
1. v ∝ x^-1

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From figure tan θ = F_c ; θ
mg

kq² = x
x² mg 2ℓ

or x³ ∝ q² …(1)
or x^{3/ 2} ∝ q …(2)
Differentiating eq. (1) w.r.t. time
3x² dx ∝ 2q dq but dq is constant
dt dt dt

so x²(v) ∝ q Replace q from eq. (2)
x²(v) ∝ x^3/2 or v ∝ x^–1/2

Correct Option: C

From figure tan θ = F_c ; θ
mg

kq² = x
x² mg 2ℓ

or x³ ∝ q² …(1)
or x^{3/ 2} ∝ q …(2)
Differentiating eq. (1) w.r.t. time
3x² dx ∝ 2q dq but dq is constant
dt dt dt

so x²(v) ∝ q Replace q from eq. (2)
x²(v) ∝ x^3/2 or v ∝ x^–1/2