Question

The voice coil of a speaker has a diameter of 0.025m, contains 55 turns of wire, and is placed in a 0.10 T magnetic field. The current in the voice coil is 2.0A . Determine the magnetic force that acts on the coil and the cone.

Answer 1

We have to find the magnitude of magnetic force acting on the coil and the cone. This magnetic force is due to the present of a current carrying loop in a magnetic field and the formula for this force is given by: $F=ILB\sin \varphi$, where ‘$\varphi$’ is the angle made by the length or direction vector with the magnetic field vector. We shall use this formula to proceed in our solution.

Complete step by step answer:
Let us first assign some terms that we are going to use later in our solution.
Let the current in the voice be denoted by ‘I’, such that the value of current is equal to 2.0 A.
Let the length of the loop of wire be ‘L’.
Let the total number of turns be denoted by ‘N’.
Let the diameter of the voice coil be ‘D’, such that the diameter is given as 0.025m.
And, let the magnetic field be denoted by ‘B’, such that it is given as 0.10 Tesla.
Now, the length of the wire loop can be calculated as:
$\begin{aligned} & \Rightarrow L=N\times \left( \pi D \right) \\\ & \Rightarrow L=55\times \left( 3.14\times 0.025 \right)m \\\ & \therefore L=4.3175m \\\ \end{aligned}$
We know that, the formula for magnetic force is given by:
$\Rightarrow F=ILB\sin \varphi$
Here, the angle between the direction vector and magnetic field is equal to ${{90}^{\circ }}$. Therefore, we have:
$\Rightarrow \sin \varphi =1$
Thus, putting the values of all the known terms in the force equation, we get:
$\begin{aligned} & \Rightarrow F=2.0\times 4.3175\times 0.10\times 1 \\\ & \therefore F=0.8635N \\\ \end{aligned}$

Hence, the magnetic force that acts on the coil and the cone comes out to be 0.8635 Newton.

Note: Whenever solving problems like these, be sure to take the correct length measurements, that is, be careful as to what is given in the problem. It may be the radius, diameter or even the perimeter. Also, be careful when finding the angle between two vector quantities as taking a wrong angle would make our entire solution incorrect.