# Magnetic induction – problems and solutions

1. The following factors influence the magnetic induction on the conductor wire.

(1) the current flowing in the wire

(2) permittivity

(3) wire density

(4) the distance of a point from the wire

Which statements are correct

Solution :

The equation of magnetic induction of a wire :

μ_{o }= Permeability of a vacuum or magnetic constant

I = Electric current flowing on the wire

r = the distance of a point from the wire

B = the magnitude of magnetic induction

2. Note the statements related to the following magnetic induction.

(1) the current flowing in the wire

(2) the permeability of a vacuum

(3) wire cross-sectional area

(4) wire density

What affects magnetic induction magnitudes on a wire conductor.

Solution

Learn the magnetic induction formula and previous description.

3. The electric current I flows on the conductor wire. What is the magnetic induction at the center of the circle (P)? (µ_{o} = 4π.10^{-7} Wb.m^{-1}.A^{-1})

__Known :__

Radius of circle (r) = 6 cm = 6 x 10^{-2} meters

Electric current (I) = 8 Ampere

Permeability of a vacuum (µ_{o}) = 4π x 10^{-7 }Wb.A^{-1} m^{-1}

__Wanted:__ the magnetic induction at the center of the circle (P)

__Solution :__

360^{o} – 90^{o} = 270^{o}. 270^{o} / 360^{o} = 3/4 then 270^{o} = 3/4 circumference

The magnetic field formula at the center of the coil with a number of loops:

*B = magnetic field, N = number of windings, I = electric current, r = radius of curvature*

In the above problem, there is only one winding so that N is removed from the equation. The wire coil on the above problem is not 1 circle but 3/4 circle. The above formula is adjusted again with this problem :

The magnetic induction at the center of the circle :

4. Current 2 A flows on a circular wire like the picture. What is the magnitude and direction of magnetic induction at point P if the radius of circle 4π cm.

__Known :__

Radius (r) = 4π cm = 4π x 10^{-2} meters

Electric current (I) = 2 Ampere

Permeability of a vacuum (µ_{o}) = 4π x 10^{-7 }Wb.A^{-1} m^{-1}

__Wanted :__ The magnitude and direction of magnetic induction at point P

__Solution :__

The wire coil on the above problem is 1/2 circle.

The magnitude of magnetic induction at point P :