A wire 2.30 m long carries a current of 13.0 A and makes an angle of 35.0^∘ with a uniform mag

A wire 2.30 m long carries a current of 13.0 A and makes...

A wire $2.30 \mathrm{~m}$ long carries a current of $13.0 \mathrm{~A}$ and makes an angle of $35.0^{\circ}$ with a uniform magnetic field of magnitude $B=1.50 \mathrm{~T}$. Calculate the magnetic force on the wire.

Key Concepts

Magnetic Force on a Current-Carrying Conductor

This concept involves the determination of the force exerted on a conductor carrying an electric current when it is placed in a magnetic field. The force is given by the formula F = I L B sin?, where I is the current, L is the length of the conductor, B is the magnetic field strength, and ? is the angle between the direction of the current and the magnetic field. This force results from the interaction between the magnetic field and the moving charges within the conductor.

Angle Dependence in Magnetic Force Calculations

The sine of the angle (sin?) in the force equation reflects how the component of the magnetic field perpendicular to the current affects the magnitude of the force. When the conductor is parallel to the magnetic field (? = 0° or 180°), the force is zero because sin? is zero, while it reaches a maximum when the current is perpendicular (? = 90°) to the magnetic field, where sin? is equal to one.

Transcript

00:01 Hello students.

00:02 The question is there is a current carrying wire having its length as 2 .3 meter and current in it is 13 .0 ampere and the magnetic field which is given is 1 .5 tesla and the wire is in such a way that it is making an angle of 35 degree with the magnetic field.

00:24 Okay.

00:26 So to imagine you this situation i will give you two examples in a 2d way and in a 3d way.

00:33 You can imagine your in a 2d way your x and y axis in which x axis i have taken as a magnetic field.

00:42 This x axis i have taken as magnetic field and the wire which is making an angle of 35 degree with the x axis.

00:52 It is also making 35 degree angle with the magnetic field.

00:57 Okay, now consider the 3d way consider your page the page you have taken on your lap it is your horizontal the magnetic field is into the paper okay the magnetic here cross shows the magnetic field is into the paper and the wire which is on the paper is making an angle of 35 degree with the x -axis of the paper or you can say it is making an angle of 35 degree with the horizontal paper.

01:30 So, now the lawrence force is given by f is equals to i, b, cross, l.

01:40 Okay? if we are removing cross product, then it is written as i, b, l, sign of theta.

01:51 Okay? here, theta is given as 35 degree.

01:55 Now, sine of theta is, sign of 35 degree is 0 .5735.

02:08 Okay.

02:12 I is 13 .0 into b is 1 .50 into length is 2 .3 into 0 .575.

02:24 The answer is coming as 25 .735...