Question

A wire $1.80$ m long carries a current of$13.0$ A and makes an angle of $35.0°$with a uniform magnetic field of magnitude$B=1.50$ T. Calculate the magnetic force on the wire.

Short answer

The magnetic force on the wire is $20.1N$.

Step-by-step solution

Listing the given quantities

• Current in the conductor,$i=13.0A$
• Magnetic field,$B=1.50T$
• Length of the conductor,$L=1.80m$
• The angle between current and field, $\theta =35°$

Understanding the concept of magnetic force

By using the formulas of magnetic force in terms of current and magnetic field and substituting the given quantities, we can find the magnitude of the magnetic force.

Formula:

Magnetic force, $F_B=iLBsin\theta$

Calculation of magnetic force on the wire

The magnetic force is given by:

$F_B=iLBsin\theta$

Where

$$\begin{gathered} i=Current,L=Lengthoftheconductor,B=Magneticfield, \\ \theta =Anglebetweencurrentandfield \end{gathered}$$

Therefore,

role="math" localid="1662458941501" $$\begin{gathered} F_B=\left(13.0\right)\left(1.80\right)\left(1.50\right)\left(\sin 35°\right) \\ =20.1\text{N} \end{gathered}$$

The magnetic force on the wire is $20.1N$.