Derive an expression for torque acting on a dipole of dipole moment p → , when it is placed in uniform external field E → .

An electric dipole having charges ± q , and of size 2 a is placed in uniform electric field vector E as shown in figure. The forces, acting on the charges are + q E → and - q E → . The net force on the dipole is F → = + q E → + ( - q E → ) = 0 Both forces provide an equivalent torque with magnitude τ = q E × Perpendicular distance (AC) τ = q | E | . 2 a sin θ τ = | P | E | sin θ The direction of the torque can be given by vector τ = P → × E → This value of torque acting on the dipole tends to align the dipole moment parallel to the electric field.

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Gamma Question Bank for Medical Physics>Chapter 16 - Electric Charges and Fields>Assignment>Q 51

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Derive an expression of electric field due to uniformly charged infinite plane sheet.

Important Questions on Electric Charges and Fields

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Gamma Question Bank for Medical Physics>Chapter 16 - Electric Charges and Fields>Assignment>Q 52

Three charges of same magnitude

q

are placed at the corners of an equilateral triangle of side length

a

. Find the net force on any one of charges.

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Gamma Question Bank for Medical Physics>Chapter 16 - Electric Charges and Fields>Assignment>Q 53

Find electric field inside a uniformly charged thin spherical shell having charge

Q

. If a charge

q

is placed at the centre of this shell, how the electric field will change?

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Gamma Question Bank for Medical Physics>Chapter 16 - Electric Charges and Fields>Assignment>Q 54

Derive an expression for torque acting on a dipole of dipole moment

\vec{p}

, when it is placed in uniform external field

\vec{E}

.

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Gamma Question Bank for Medical Physics>Chapter 16 - Electric Charges and Fields>Assignment>Q 55

(a) Explain the invariant property of charge.
(b) Draw the electric field lines for a dipole.

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Gamma Question Bank for Medical Physics>Chapter 16 - Electric Charges and Fields>Assignment>Q 56

Derive an expression for electric field inside a solid non-conducting sphere of charge

Q

, when the charge is distributed uniformly. Also calculate electric field at the centre of sphere and electric field on the surface of sphere.

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Gamma Question Bank for Medical Physics>Chapter 16 - Electric Charges and Fields>Assignment>Q 57

Derive the expression for electric field on the axis of an electric dipole.

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Gamma Question Bank for Medical Physics>Chapter 16 - Electric Charges and Fields>Assignment>Q 58

What is meant by the statement that the electric field of a point charge has spherical symmetry whereas that of a linear charge of large length is cylindrically symmetrical?

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Gamma Question Bank for Medical Physics>Chapter 16 - Electric Charges and Fields>Assignment>Q 59

(a) A copper sphere of mass