Question

an electric dipole 4 is kept at coordinate points (1,0,4) are kept at (2,-1,5) the eletric field is given by e=20 calculate the torque

Answer 1

Therefore torque $=80\times 10^{-6} (\hat k- \hat j)$

Explanation:

[The unit of electric dipole is not given I consider μC as unit of  electric dipole and $e=20\hat i NC^{-1}$]

Dipole : The magnitude of electric dipole moment is product of charge and distance.

Electric field: Electric field is

• directly proportional to product of the magnitude of point charge  and the magnitude of Q charge.
• inversely proportional to the square of the magnitude of distance between the unit charge and Q.

$e=k\frac{Q}{r^2}$        [ k =constant]

Torque: The product of potential energy and electric field.

Given points are A(1,0,4) and B(2,-1,5)

$\overrightarrow {OA}= \hat i+0 \hat j+4\hat k$

$\overrightarrow {OB}= 2\hat i- \hat j+5\hat k$

$D=\overrightarrow {OB} -\overrightarrow {OA}$

    $= 2\hat i- \hat j+5\hat k- (\hat i+0 \hat j+4\hat k)$

    $=\hat i- \hat j+\hat k$

q= 4 μC = (4×10⁻⁶)C

Potential energy P= q×d

                              $=4\times10^{-6}(\hat i- \hat j+\hat k)$

$e=20\hat i NC^{-1}$

Torque   $\tau= P\times e$

                 $=4\times10^{-6}(\hat i- \hat j+\hat k) \times20\hat i$

                $=80\times 10^{-6} (\hat k- \hat j)$

Therefore torque $=80\times 10^{-6} (\hat k- \hat j)$