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An electric dipole consist of charges …

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An electric dipole consist of charges 2×10* -8 , separated by a distance of 2 mm , it is placed near a long line charge of density = 4× 10* -4 . calculate the net force acting on the dipole and also it's direction
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Sia ? 6 years, 3 months ago

Electric field intensity at a distance r from line charge of density {tex}\lambda {/tex} is
{tex}E = \frac{\lambda }{{2\pi {\varepsilon _0}r}}{/tex}
{tex}\therefore {/tex} Field intensity on negative charge (r = 0.02 m)
{tex}{E_1} = \frac{{4 \times {{10}^{ - 4}} \times 9 \times {{10}^9} \times 2}}{{0.02}} = 3.6 \times {10^8}N/C{/tex}
Force on negative charge
{tex}{F_1} = q{E_1} = 2 \times {10^{ - 8}}\left( {3.6 \times {{10}^8}} \right) = 7.2N{/tex}
It is directed towards the line charge.
Similarly field intensity at positive charge (r = 0.022 m)
{tex}{E_2} = \frac{{4 \times {{10}^{ - 4}} \times 9 \times {{10}^9} \times 2}}{{0.022}} = 3.27 \times {10^8}N/C{/tex}
Force on positive charge
{tex}{F_2} = q{E_2} = 2 \times {10^{ - 8}}(3.27 \times {10^8}) = 6.54N{/tex}
It is directed away from the line charge.
{tex}\therefore {/tex}Net force on the dipole,
F = F1 - F2 = (7.2 - 6.54)N = 0.66 N
F is towards the line charge.

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