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Solve this question based on magnetic field of a finite straight wire

Solve this question based on magnetic field of a finite straight wire

Question Image
Grade:12

2 Answers

Eshan
askIITians Faculty 2095 Points
2 years ago
We need to find the angles the lines OP and OQ form with OM. Let them be\theta_1and\theta_2, respectively.

From trigonometry,tan\theta_1=\dfrac{3}{4}\implies sin\theta_1=\dfrac{3}{5}
andtan\theta_2=\dfrac{4}{3}\implies sin\theta_2=\dfrac{4}{5}

Hence magnetic field at point O=\dfrac{\mu_0i}{2\pi a}\dfrac{sin\theta_1+sin\theta_2}{2}
=\dfrac{\mu_0i}{4\pi a}
Khimraj
3007 Points
2 years ago
 
Magnetic field due to a wire of finite length is given by
B = (uoI/4\pir)(sin\Theta 1 + sin\Theta 2)
where \Theta 2 is angle QOM
and \Theta 1 is angle POM
r is perpendicular distance
So B = (uoI/4\pia)(3/5 + 4/5)
So B = (7/20)uoI/\pia.
Hope it clears. If you like answer then please approve it.

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