Question

An electric dipole of dipole moment 2i+3j placed under electric field of 3i+j+4k,find net toque on a diapole​

Answer 1

Given:

• dipole moment = 2i+3j
• electric field = 3i+j+4k

To find :

• net toque on the dipole

Formula used :

$\bf \tau = p \times e$

$\sf \:where : - \\\sf \tau = torque \\ \sf p = dipole \: moment \\ \sf e = electric \: field$

Solution :

$\sf \implies\tau = p \times e$

Put :-

• dipole moment (p) = 2i+3j
• electric field(e) = 3i+j+4k

$\sf \implies\tau =( 2i + 3j + 0k)\times (3i + j + 4k)$

Now, we can find by using determinant :-

$\implies\left[ \begin{array}{ccc} \sf i&\sf j& \sf k\\2&3&0\\3&1&4\end{array}\right]$

$\sf \implies i \left[\begin{array}{cc}3&0 \\ 1&4\\\end{array}\right] -j\left[\begin{array}{cc}2&0 \\ 3&4\\\end{array}\right] +k\left[\begin{array}{cc}2&3 \\ 3&1\\\end{array}\right]$

$\sf \implies i(12 - 0) - j(8 - 0) + k(2 - 9)$

$\sf \implies 12i - 8 j - 7k$

$\sf \implies \tau = 12i - 8 j - 7k$

Answer :

Net toque on the dipole =( 12i-8j-7 k ) Nm