Q. 495.0( 1 Vote )

# A long, cylindrical wire of radius b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnetic field at a point inside the wire at a distance a from the axis.

Given:

Current distributed throughout the cross section = i

Diagram: Formula used:

Ampere’s circuital law states that the line integral of the magnetic field for a closed surface is μ0 times the current enclosed by the surface. , where B = magnetic field, dl = line element, μ0 = magnetic permeability of vacuum, I = current enclosed.

Since the current i is uniformly distributed throughout the cross section of the wire,

For an amperian loop of radius a(a<b) from the center of the wire,

I (current enclosed) Where

i= total current distributed throughout the wire,

b = radius of the wire,

a = distance from the axis at which the magnetic field is to be found.

Hence, from Ampere’s circuital law, since 2πa = circumference of Amperian loop of radius a, and I = enclosed current = ia2/b2.

Therefore, magnetic field at a distance a from the axis inside the wire, Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Magnetic field due to current carrying straight wire37 mins  Magnetic field due to current carrying circular loop36 mins  Interactive Quiz on Magnetic field due to straight wire & circular loop41 mins  Gain Confidence on Magnetic Effects of Current with Questions41 mins  Equation of electric and magnetic field52 mins  Magnetic force on moving charge particle in magnetic field | Quiz32 mins  Magnetic force on moving charge particle in magnetic field44 mins  Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)47 mins  Few Applications of Gauss's law54 mins  10 Problems on related to Electric Field & Charges41 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 