Magnetic Force On A Current Carrying Wire

To find the force acting on a current-carrying wire placed in a magnetic field, we use the formula for the magnetic force on a current segment: $%5Cvec%7BF%7D%20%3D%20I%20(%5Cvec%7BL%7D%20%5Ctimes%20%5Cvec%7BB%7D)$ .

Given:

Current, $I%20%3D%200.5%20%5C%2C%20%5Ctext%7BA%7D$
Length of the wire, $L%20%3D%201%20%5C%2C%20%5Ctext%7Bcm%7D%20%3D%200.01%20%5C%2C%20%5Ctext%7Bm%7D$
Direction along $%2Bx$ , so $%5Cvec%7BL%7D%20%3D%200.01%20%5C%2C%20%5Chat%7Bi%7D%5C%2C%20%5Ctext%7Bm%7D$
Magnetic field, $%5Cvec%7BB%7D%20%3D%20(0.4%20%5C%2C%20%5Ctext%7BmT%7D%20%5Chat%7Bj%7D)%20%2B%20(0.6%20%5C%2C%20%5Ctext%7BmT%7D%20%5Chat%7Bk%7D)$
Convert $%5Ctext%7BmT%7D$ to $%5Ctext%7BT%7D$ : $1%20%5C%2C%20%5Ctext%7BmT%7D%20%3D%2010%5E%7B-3%7D%20%5C%2C%20%5Ctext%7BT%7D$
Thus, $%5Cvec%7BB%7D%20%3D%20(0.4%20%5Ctimes%2010%5E%7B-3%7D%20%5Chat%7Bj%7D%20%2B%200.6%20%5Ctimes%2010%5E%7B-3%7D%20%5Chat%7Bk%7D)%20%5C%2C%20%5Ctext%7BT%7D$

The cross product $%5Cvec%7BL%7D%20%5Ctimes%20%5Cvec%7BB%7D$ is:

$%5Cvec%7BL%7D%20%5Ctimes%20%5Cvec%7BB%7D%20%3D%20(0.01%20%5C%2C%20%5Chat%7Bi%7D)%20%5Ctimes%20%5B(0.4%20%5Ctimes%2010%5E%7B-3%7D%20%5Chat%7Bj%7D)%20%2B%20(0.6%20%5Ctimes%2010%5E%7B-3%7D%20%5Chat%7Bk%7D)%5D$

The cross products are:

$(%5Chat%7Bi%7D%20%5Ctimes%20%5Chat%7Bj%7D)%20%3D%20%5Chat%7Bk%7D$

$(%5Chat%7Bi%7D%20%5Ctimes%20%5Chat%7Bk%7D)%20%3D%20-%5Chat%7Bj%7D$

So,

$%5Cvec%7BL%7D%20%5Ctimes%20%5Cvec%7BB%7D%20%3D%200.01%20%5C%7B(0.4%20%5Ctimes%2010%5E%7B-3%7D)%20%5Chat%7Bk%7D%20-%20(0.6%20%5Ctimes%2010%5E%7B-3%7D)%20%5Chat%7Bj%7D%5C%7D$

$%5Cvec%7BL%7D%20%5Ctimes%20%5Cvec%7BB%7D%20%3D%20(0.4%20%5Ctimes%2010%5E%7B-5%7D%20%5Chat%7Bk%7D%20-%200.6%20%5Ctimes%2010%5E%7B-5%7D%20%5Chat%7Bj%7D)$

Now, compute $%5Cvec%7BF%7D%20%3D%20I%20(%5Cvec%7BL%7D%20%5Ctimes%20%5Cvec%7BB%7D)$ :

$%5Cvec%7BF%7D%20%3D%200.5%20(0.4%20%5Ctimes%2010%5E%7B-5%7D%20%5Chat%7Bk%7D%20-%200.6%20%5Ctimes%2010%5E%7B-5%7D%20%5Chat%7Bj%7D)$

$%5Cvec%7BF%7D%20%3D%20(0.2%20%5Ctimes%2010%5E%7B-5%7D%20%5Chat%7Bk%7D%20-%200.3%20%5Ctimes%2010%5E%7B-5%7D%20%5Chat%7Bj%7D)$

$%5Cvec%7BF%7D%20%3D%20(2%20%5Chat%7Bk%7D%20-%203%20%5Chat%7Bj%7D)%20%5Ctimes%2010%5E%7B-6%7D%20%5Ctext%7BN%7D$

Expressing in $%5Cmu%5Ctext%7BN%7D$ :

$%5Cvec%7BF%7D%20%3D%20(-3%20%5Chat%7Bj%7D%20%2B%202%20%5Chat%7Bk%7D)%20%5C%2C%20%5Cmu%5Ctext%7BN%7D$

The force acting on the segment is $(-3%20%5Chat%7Bj%7D%20%2B%202%20%5Chat%7Bk%7D)%20%5C%2C%20%5Cmu%5Ctext%7BN%7D$ .

About Magnetic Force On A Current Carrying Wire - CBSE-CLASS-XII

Magnetic Force On A Current Carrying Wire is a vital chapter for CBSE-CLASS-XII aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.

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Review the topic breakdown to see which sub-topics within Magnetic Force On A Current Carrying Wire carry the most weight. Then, tackle the questions iteratively to solidify your understanding.

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

About Magnetic Force On A Current Carrying Wire - CBSE-CLASS-XII

Frequently Asked Questions

Why focus on Magnetic Force On A Current Carrying Wire PYQs?

How to best use this analysis?

Magnetic Force On A Current Carrying Wire

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

About Magnetic Force On A Current Carrying Wire - CBSE-CLASS-XII

Frequently Asked Questions

Why focus on Magnetic Force On A Current Carrying Wire PYQs?

How to best use this analysis?

Chapter Questions
1 MCQs