Chapter 20, Problem 54P

A circular coil 12.0 cm in diameter and containing nine loops lies flat on the ground. The Earth's magnetic field at this location has magnitude 5.50 x 10-⁵T and points into the Earth at an angle of 56.0° below a line pointing due north. If a 7.20-A clockwise current passes through the coil, (a) determine the torque on the coil, and (b) which edge of the coil rises up: north, east, south, or west?

To determine

(a) To Determine:

The torque on the coil ($\text{τ}$)

Answer to Problem 54P

Solution:

The torque on the coil ($\text{τ}$)is $\text{2}{\text{.25×10}}^{\text{-5}}\text{N}\text{.m}$.

Explanation of Solution

Given Info:

The diameter d of the coil 12 cm or 0.12 m

The number of loops N is 9.

The current I pass through the coil is 7.20 A.

The Earth’s magnetic field B is $\text{5}{\text{.50×10}}^{\text{-5}}\text{T}$.

The angle between magnetic field and area vector $\text{θ}$ is (90⁰ -56.0⁰)

The formula to calculate the torque is

$\begin{array}{l}\text{τ}\text{=NIABsinθ}\\ \text{τ}\text{=NI}\left(\frac{{\text{πd}}^{\text{2}}}{\text{4}}\right)\text{Bsinθ}\end{array}$

• ‘ $\text{τ}$’ is the torque.

• ‘N, is the Number of turns of coil.

• ‘d’ is the diameter of coil.

• ‘B’ is the Earth’s magnetic field.

Substitute 9 for ‘N’, 7.20A for ‘I’, 0.12m for ‘d’ and $\text{5}{\text{.50×10}}^{\text{-5}}\text{T}$ for ‘B’, to find $\text{τ}$

$\text{τ}\text{=9×(7}\text{.20A)×}\left(\frac{\text{π×}{\left(\text{0}\text{.12}\text{m}\right)}^{\text{2}}}{\text{4}}\right)\text{×}\left(\text{5}{\text{.50×10}}^{\text{-5}}\text{T}\right){\text{sin(90}}^{\text{0}}\text{-56}{\text{.0}}^{\text{0}}\text{)}$

$\text{τ}\text{= 2}{\text{.25×10}}^{\text{-5}}\text{N}\text{.m}$

To determine

(b) To Determine:

The direction of coil rise.

Answer to Problem 54P

Solution:

The coil rises up towards north.

Explanation of Solution

The torque is positive i.e. it is directed outward to the plane and magnetic field is pointing into the Earth below a line point due north. According to right hand rule the coil will rise up in north direction.