Question

A rectangular current loop (a = 16.0 cm, b = 30.0 cm) is located a distance d = 14.0 cm near a long, straight wire that carries a current ( I W ) (IW) of 10.0 A (see the drawing). The current in the loop is I L IL = 20.0 A. Determine the magnitude of the net magnetic force that acts on the loop.

Answer 1

Answer:

The magnitude of the net magnetic force is $3.12\times10^{-5}\ N$

Explanation:

Given that,

Distance = 14.0 cm

Side a = 16.0 cm

Side b = 30.0 cm

Current $I_{w}=10.0\ A$

Current $I_{L}=20.0\ A$

According to figure,

Force F₂ and F₄  balance by each other

So, We need to calculate the magnetic force

Using formula of magnetic force

$F_{1}=\dfrac{\mu_{0}}{4\pi}\times\dfrac{2I_{L}I_{\omega}}{d}\times a$

Put the value into the formula

$F_{1}=\dfrac{10^{-7}\times2\times20\times10}{14.0\times10^{-2}}\times16.0\times10^{-2}$

$F_{1}=4.57\times10^{-5}\ N$

The direction of force is downward.

For F₃,

$F_{3}=\dfrac{10^{-7}\times2\times20\times10}{44\times10^{-2}}\times16.0\times10^{-2}$

$F_{3}=1.45\times10^{-5}\ N$

We need to calculate the magnitude of the net magnetic force that acts on the loop

Using formula of net magnetic force

$F=F_{1}-F_{3}$

Put the value into the formula

$F=4.57\times10^{-5}-1.45\times10^{-5}$

$F=3.12\times10^{-5}\ N$

The direction of net force towards the wire.

Hence, The magnitude of the net magnetic force is $3.12\times10^{-5}\ N$