
A magnetic field due to a long straight wire carrying a current is proportional to
A.
B.
C.
D.
Answer
492.6k+ views
2 likes
Hint: Apply Biot- savart’s law by considering an elementary length on the finite straight wire. For the long or infinite length of the straight wire or any conductor, the perpendicular distance from the wire is at the center of the wire that .
Complete step by step solution:
Let us consider an straight wire through which current flows and a point , which lies at a perpendicular distance from the wire as shown in the diagram below:
Now let be a small current carrying element at distance from the point and the angle between distances and be . The length between the center of the wire and elementary length is .
Now we apply Bio- savart’s law, the magnetic field due to the current element at point is,
… (I)
From the triangle formed by ,
… (II)
And
Now differentiate above equation with respect to , we get,
… (III)
Now we substitute the values of and using equation (II) and (III), we have,
Now we integrate from to the above equation,
After further simplifying, we get,
It is given in the question that the straight wire is long that is infinite, in this the point always be at the center of the straight wire. So, the angle and will be equal to .
Now substitute and as in the above expression.
Since is a constant quantity, so the above expression can be written as,
Thus, the magnetic field ( ) due to a long straight wire carrying a current ( ) is proportional to
So, the correct answer is “Option A”.
Note:
Be careful while answering because the formula for finite straight wire and infinite straight is completely different.
When wire has finite length:
When wire has infinite length, :
When wire has infinite length and point lies at near wire’s end, :
Complete step by step solution:
Let us consider an straight wire through which current

Now let
Now we apply Bio- savart’s law, the magnetic field due to the current element
From the triangle formed by
And
Now differentiate above equation with respect to
Now we substitute the values of
Now we integrate from
After further simplifying, we get,
It is given in the question that the straight wire is long that is infinite, in this the point
Now substitute
Since
Thus, the magnetic field (
So, the correct answer is “Option A”.
Note:
Be careful while answering because the formula for finite straight wire and infinite straight is completely different.
When wire has finite length:
When wire has infinite length,
When wire has infinite length and point
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Earth rotates from West to east ATrue BFalse class 6 social science CBSE

The easternmost longitude of India is A 97circ 25E class 6 social science CBSE

Write the given sentence in the passive voice Ann cant class 6 CBSE

Convert 1 foot into meters A030 meter B03048 meter-class-6-maths-CBSE

What is the LCM of 30 and 40 class 6 maths CBSE

What is history A The science that tries to understand class 6 social science CBSE

Trending doubts
Father of Indian ecology is a Prof R Misra b GS Puri class 12 biology CBSE

Who is considered as the Father of Ecology in India class 12 biology CBSE

Enzymes with heme as prosthetic group are a Catalase class 12 biology CBSE

A deep narrow valley with steep sides formed as a result class 12 biology CBSE

An example of ex situ conservation is a Sacred grove class 12 biology CBSE

An orchid growing as an epiphyte on a mango tree is class 12 biology CBSE
