Two opposite and equal charges 4 × 10-8 coulomb when placed 2 × 10-2 cm away, form a dipole. If this dipole is placed in an external electric field 4 × 108 newton/ coulomb, the value of maximum torque and the work done in rotating it through 180° will be

Question

Two opposite and equal charges 4 × 10-8 coulomb when placed 2 × 10-2 cm away, form a dipole. If this dipole is placed in an external electric field 4 × 108 newton/ coulomb, the value of maximum torque and the work done in rotating it through 180° will be (A) 64 × 10-4 Nm and 64 × 10-4 J (B) 32 × 10-4 Nm and 32 × 10-4 J (C) 64 × 10-4 Nm and 32 × 10-4 J (D) 32 × 10-4 Nm and 64 × 10-4 J

Tardigrade Admin · Accepted Answer

Dipole moment p=4 × 10-8 × 2 × 10-4 =8 × 10-12 m Maximum torque =p E=8 × 10-12 × 4 × 108 =32 × 10-4 Nm Work done in rotating through 180°=2 p E =2 × 32 × 10-4=64 × 10-4 J

$64 \times 1 0^{- 4} N m$ and $64 \times 1 0^{- 4} J$

$32 \times 1 0^{- 4} N m$ and $32 \times 1 0^{- 4} J$

$64 \times 1 0^{- 4} N m$ and $32 \times 1 0^{- 4} J$

$32 \times 1 0^{- 4} N m$ and $64 \times 1 0^{- 4} J$

Dipole moment $p = 4 \times 1 0^{- 8} \times 2 \times 1 0^{- 4}$
$= 8 \times 1 0^{- 12} m$
Maximum torque $= pE = 8 \times 1 0^{- 12} \times 4 \times 1 0^{8}$
$= 32 \times 1 0^{- 4} N m$
Work done in rotating through $18 0^{\circ} = 2 pE$
$= 2 \times 32 \times 1 0^{- 4} = 64 \times 1 0^{- 4} J$

Q. Two opposite and equal charges 4×10−8 coulomb when placed 2×10−2cm away, form a dipole. If this dipole is placed in an external electric field 4×108 newton/ coulomb, the value of maximum torque and the work done in rotating it through 180∘ will be

64×10−4Nm and 64×10−4J

32×10−4Nm and 32×10−4J

64×10−4Nm and 32×10−4J

32×10−4Nm and 64×10−4J

Dipole moment p=4×10−8×2×10−4 =8×10−12m Maximum torque =pE=8×10−12×4×108 =32×10−4Nm Work done in rotating through 180∘=2pE =2×32×10−4=64×10−4J

$64 \times 1 0^{- 4} N m$ and $64 \times 1 0^{- 4} J$

$32 \times 1 0^{- 4} N m$ and $32 \times 1 0^{- 4} J$

$64 \times 1 0^{- 4} N m$ and $32 \times 1 0^{- 4} J$

$32 \times 1 0^{- 4} N m$ and $64 \times 1 0^{- 4} J$

Dipole moment $p = 4 \times 1 0^{- 8} \times 2 \times 1 0^{- 4}$
$= 8 \times 1 0^{- 12} m$
Maximum torque $= pE = 8 \times 1 0^{- 12} \times 4 \times 1 0^{8}$
$= 32 \times 1 0^{- 4} N m$
Work done in rotating through $18 0^{\circ} = 2 pE$
$= 2 \times 32 \times 1 0^{- 4} = 64 \times 1 0^{- 4} J$