First slide

Force on a current carrying wire placed in a magnetic field

Question

A parabolic section of wire OA is located in the x-y plane and carries current I = 12 A. A uniform magnetic field B = 4.0 T making an angle 60⁰ with x axis exists in x-y plane. Calculate the magnetic force on the wire OA. Coordinates of A are (0.25 m, 1 m).

Moderate

A

$6 (\sqrt{3} - 4 k) \hat{k} N$
B

$6 (4 - \sqrt{3}) \hat{k} N$
C

$3 (\sqrt{3} - 4) \hat{k} N$
D

$3 (4 - \sqrt{3}) \hat{k} N$

Solution

Magnetic field is uniform, apply $\vec{F} = l \vec{L} \times \vec{B}$
$where \vec{L} = 0 .25 \hat{i} + \hat{j} and \vec{B} = 4 (\cos 60 \hat{i} + \sin 60 \hat{j}) = 2 \hat{i} + 2 \sqrt{3} \hat{j}$
Therefore $\vec{F} = 6 (\sqrt{3} - 4) \hat{k} N$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App