# 1. Find the current through a loop needed to create a maximum torque of 9.00 Nm. The loop has 50...

## Question:

1. Find the current through a loop needed to create a maximum torque of 9.00 Nm. The loop has 50 square turns that are 15.0 cm on a side and is in a uniform 0.800 T magnetic field.

2. Calculate the magnetic field strength needed on a 200 turn square loop 20.0 cm on a side to create a maximum torque of 300 Nm if the loop is carrying 25.0 A.

## Torque on a Current Loop in a Magnetic Field

The magnetic torque exerted on a current carrying loop in a uniform magnetic field is given by,

{eq}\tau=nIAB\sin\theta {/eq}

Where,

• {eq}n {/eq} is the number of turns
• {eq}B {/eq} is the magnetic field intensity,
• {eq}I {/eq} is the current through the wire,
• {eq}A {/eq} is the area of the loop.

1)

Given:

{eq}\tau=9.00\ Nm\\ n=50\\ A=0.15\times0.15\ m^2=0.0225\ m^2\\ B=0.800\ T {/eq}

The Current needed is,

{eq}\displaystyle I=\frac{\tau}{nAB}=\frac{9.00}{50\times0.0225\times0.800}\ A=10\ A {/eq}

2)

Given:

{eq}n=200\\ A=0.200^2\ m^2=0.0400\ m^2\\ \tau=300\ Nm\\ I=25.0\ A {/eq}

The required magnetic field is,

{eq}\displaystyle B=\frac{\tau}{nIA}=\frac{300}{200\times25.0\times0.0400}\ T=1.5\ T {/eq} 