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An electric dipole with dipole moment 4...

An electric dipole with dipole moment `4xx 10^(-9) ` C-m is aligned at ` 30^(@) ` with the direction of a uniform electric field of magnitude ` 5xx 10^(4) NC^(-1) `.Calculate the magnitude of the torque acting on the dipole.

Text Solution

Verified by Experts

Here `p=4 xx10 ^(-9) C-m ,theta =30^(@) and E=5xx 10^(4) NC^(-1) `
` therefore ` Magnitude of torque ` tau =pE sin theta =4xx 10^(-9) xx 5xx 10^(4) xx sin 30^(@) = 4xx 10^(-9) xx 5xx 10^(4) xx 0.5 =10^(-4) N-m `
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An electrtic dipole with dipole moment 4xx10^(-9) C m is aligned at 30^(@) with the direction of a uniform electric field of magnitude 5xx10^(4) NC^(-1) . Calculate the magnitude of the torque acting on the dipole .

An electric dipole of length 10cm having charges +- 6xx10^(-3) C , placed at 30^(@) with respect to a uniform electric field experiences a torque of magnitude 6 sqrt(3) N-m . Calculate (i) magnitude of electric field (ii) the potential energy of dipole.

Knowledge Check

  • An uniform electric field of magnitude 5 xx 10^(4) NC^(-1) has a dipole of dipole moment 4xx 10^(-9) cm aligned at 30^(@) with the direction of field. Calculate the magnitude of torque acting on the dipole:

    A
    `10^(-4)Nm`
    B
    `2xx10^(-3)Nm`
    C
    `2xx10^(-5)Nm`
    D
    `10^(-5)Nm`

  • An electric dipole in a uniform electric field has potential energy U. The magnitude of the torque acting on the dipole due to the field is tau .

    A
    U is minimum and `tau` is zero when the dipole is perpendicular to the field.
    B
    U is zero and `tau` is a maximum when the dipole is perpendicular to the field.
    C
    U is a minimum and `tau` is a maximum when the dipole is perpendicular to the field.
    D
    U is a minimum and `tau` is zero when the dipole is anti-parallel to the field.

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    When an electric dipole of moment | vec(p) | = q xx 2a is held at an angle theta , with the direction of uniform external electric field vec(E) , a torque tau = pE sin theta acts on the dipole. This torque tries to align the electric dipole in the direction of the field. When vec(p) is along vec(E), theta^(@) , tau = pE sin 0^(@) = zero . The dipole is in stabel equilibrium. The energy possessed by the dipole by virtue of its particular position in the electric field is called potential energy of dipole. U = W = -pE (cos theta_(2) - cos theta_(1)) theta_(1) = 90^(@) is the position of zero potential energy. :. U = W = -pE (cos theta - cos 90^(@)) = -pE cos theta . For stable equillibrium, theta 0^(@), :. U = -pE = minimum. Read the above passage and answer the following questions : (i) What is the direction of torque acting on electric dipole held at an angle with uniform external electric field ? (ii) An electric dipole of length 10cm having charges +- 6xx10^(-3) C , placed at 30^(@) with respect to a uniform electric field experiences a torque of magnitude 6 sqrt(3) N-m . Calculate. (a) magnitude of electric field. (b) potential energy of dipole. (iii) What is the physical significance of this concept in our day to day life ?

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