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

The magnitude of the net magnetic force is
`3.12*10^(-5)\ N`

Step-by-step 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)=(\mu_(0))/(4\pi)*(2I_(L)I_(\omega))/(d)* a`

Put the value into the formula

`F_(1)=(10^(-7)*2*20*10)/(14.0*10^(-2))*16.0*10^(-2)`

`F_(1)=4.57*10^(-5)\ N`

The direction of force is downward.

For F₃,

`F_(3)=(10^(-7)*2*20*10)/(44*10^(-2))*16.0*10^(-2)`

`F_(3)=1.45*10^(-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*10^(-5)-1.45*10^(-5)`

`F=3.12*10^(-5)\ N`

The direction of net force towards the wire.

Hence, The magnitude of the net magnetic force is
`3.12*10^(-5)\ N`