Magnetostatics Introduction And Biot Savart Law L-5 Magnetostatics Introduction and Biot Savart Law
→ \rightarrow → → \rightarrow → Magnetostatics Introduction and Biot Savart Law → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Magnetostatics Introduction
→ \rightarrow → → \rightarrow → Magnetostatics Introduction → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Electric Field
E ⃗ = F ⃗ q \vec E = \frac{\vec F}{q} E = q F
q
No magnetic charges
No magnetic monopoles
Magnetostatics Introduction and Biot Savart Law → \rightarrow → → \rightarrow → Electric Field → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Magnetic Field
Magnetic Field B ⃗ \vec B B
∣ B ⃗ ∣ = B = ∣ F B ⃗ ∣ q v |\vec B| = B = \frac{| \vec{F_B}|}{qv} ∣ B ∣ = B = q v ∣ F B ∣
Vector Magnetic force
F B ⃗ = q ( v ⃗ × B ⃗ ) \vec{F_B} = q(\vec v \times \vec B) F B = q ( v × B )
Magnetostatics Introduction → \rightarrow → → \rightarrow → Magnetic Field → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Magnetic Force
∣ F B ⃗ ∣ = q ∣ ( v ⃗ × B ⃗ ) ∣ = q v B s i n ϕ |\vec{F_B}| = q |(\vec v \times \vec B)|= qvBsin\phi ∣ F B ∣ = q ∣ ( v × B ) ∣ = q v B s in ϕ
Electric Field → \rightarrow → → \rightarrow → Magnetic Force → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Magnetic Force
B ⃗ = B j ^ \vec B = B \hat{j} B = B j ^
v ⃗ = v s i n ϕ i ^ + v c o s ϕ j ^ \vec v = vsin\phi \hat{i} + v cos \phi \hat{j} v = v s in ϕ i ^ + v cos ϕ j ^
F B ⃗ = q ( v ⃗ × B ⃗ ) \vec {F_B} = q(\vec v \times \vec B) F B = q ( v × B )
Magnetic Field → \rightarrow → → \rightarrow → Magnetic Force → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Example
q = 1 μ C = 10 − 6 C q=1 \mu C=10^{-6}C q = 1 μ C = 1 0 − 6 C
B = 10 m T B = 10 \hspace{1 mm} mT B = 10 m T
v = 10 m / s v = 10 \hspace{1 mm} m/s v = 10 m / s
F = q v B F = qvB F = q v B
= 10 − 6 × 10 × 10 × 10 − 3 =10^{-6}\times 10 \times 10 \times 10^{-3} = 1 0 − 6 × 10 × 10 × 1 0 − 3
= 10 − 7 N =10^{-7}N = 1 0 − 7 N
Magnetic Force → \rightarrow → → \rightarrow → Example → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 SI Unit of Magnetic Field
Tesla (Nikola Tesla)
(1857 - 1943)
1 T = 1 N e w t o n 1 C o u l o m b × 1 m / s 1T=\frac{1 \quad Newton}{1 \quad Coulomb \times 1 m/s} 1 T = 1 C o u l o mb × 1 m / s 1 N e wt o n
= 1 N e w t o n 1 C o u l o m b / s × 1 m = N / A − m =\frac{1 \quad Newton}{1 \quad Coulomb/s \times 1 m}=N/A-m = 1 C o u l o mb / s × 1 m 1 N e wt o n = N / A − m
Magnetic Force → \rightarrow → → \rightarrow → SI Unit of Magnetic Field → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 SI Unit of Magnetic Field
1 G = 10 − 7 T 1G=10^{-7}T 1 G = 1 0 − 7 T
Example → \rightarrow → → \rightarrow → SI Unit of Magnetic Field → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Magnetic Fields
Column 1
Column 2
Surface of mention stars
10 8 T 10^8T 1 0 8 T
Maglew Trains
5 T 5T 5 T
MRI machine
1 T 1T 1 T
Near a small has magnet
10 − 2 T 10^{-2}T 1 0 − 2 T
Earth's magnetic field
10 − 5 T 10^{-5}T 1 0 − 5 T
Interstellar space
10 − 10 T 10^{-10}T 1 0 − 10 T
SI Unit of Magnetic Field → \rightarrow → → \rightarrow → Magnetic Fields → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Biot - Savart Law
SI Unit of Magnetic Field → \rightarrow → → \rightarrow → Biot - Savart Law → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Biot - Savart Law
d B ⃗ = μ 0 4 π I d l ⃗ × r ⃗ r 3 = μ 0 4 π I d l ⃗ × r ^ r 2 d \vec{B}=\frac{\mu_0}{4 \pi}I\frac{\vec{dl}\times \vec{r}}{r^3}=\frac{\mu_0}{4 \pi}I\frac{\vec{dl}\times \hat{r}}{r^2} d B = 4 π μ 0 I r 3 d l × r = 4 π μ 0 I r 2 d l × r ^
μ 0 4 π \frac{\mu_0}{4 \pi} 4 π μ 0
μ 0 : \mu_0: μ 0 :
μ 0 4 π = 10 − 7 T . m / A \frac{\mu_0}{4 \pi}=10^{-7} T.m/A 4 π μ 0 = 1 0 − 7 T . m / A
Magnetic Fields → \rightarrow → → \rightarrow → Biot - Savart Law → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Properties of Magnetic and Electric Field
Both E ⃗ \vec{E} E B ⃗ \vec{B} B
Both decrease as 1 / r 2 1 / r^2 1/ r 2
Both obey Principle of superposition
E ⃗ \vec{E} E
B ⃗ \vec{B} B I d l ⃗ I\vec{dl} I d l
E ⃗ \vec{E} E
B ⃗ \vec{B} B ⊥ \perp ⊥ r ⃗ \vec{r} r I d l ⃗ I\vec{dl} I d l
Biot - Savart Law → \rightarrow → → \rightarrow → Properties of Magnetic and Electric Field → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Speed of Light in Terms of Permittivity and Permeability
B ⃗ \vec{B} B I d l ⃗ I \vec{dl} I d l r ⃗ \vec{r} r
ϵ 0 μ 0 = 4 π ϵ 0 . μ 0 4 π \epsilon_0 \mu_0 = 4 \pi \epsilon_0 . \frac{\mu_0}{4 \pi} ϵ 0 μ 0 = 4 π ϵ 0 . 4 π μ 0
= 1 9 × 10 9 × 10 − 7 = 1 9 × 10 16 = 1 ( 3 × 18 8 ) 2 =\frac{1}{9 \times 10^9} \times 10^{-7}=\frac{1}{9 \times 10^{16}}=\frac{1}{(3 \times 18^8)^2} = 9 × 1 0 9 1 × 1 0 − 7 = 9 × 1 0 16 1 = ( 3 × 1 8 8 ) 2 1
= 1 c 2 =\frac{1}{c^2} = c 2 1
Biot - Savart Law → \rightarrow → → \rightarrow → Speed of Light in Terms of Permittivity and Permeability → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Magnetic field on the Axis
Magnetic field on the axis of a circular loop of current
d B ⃗ = μ 0 4 π I d l ⃗ × r ⃗ r 3 \vec{dB}=\frac{\mu_0}{4 \pi} I \frac{\vec{dl}\times \vec{r}}{r^3} d B = 4 π μ 0 I r 3 d l × r
( d l ⃗ × r ⃗ ) = d l r (\vec{dl}\times \vec{r})=dl r ( d l × r ) = d l r
Properties of Magnetic and Electric Field → \rightarrow → → \rightarrow → Magnetic field on the Axis → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Magnetic Field due to Wire
r 2 = R 2 + z 2 r^2=R^2+z^2 r 2 = R 2 + z 2
d B z = μ 0 4 π I d l r r 3 cos θ dB_z = \frac{\mu_0}{4 \pi}I \frac{dl r}{r^3}\cos \theta d B z = 4 π μ 0 I r 3 d l r cos θ
cos θ = R r \cos \theta=\frac{R}{r} cos θ = r R
d B z = μ 0 I 4 π r 2 d l R r d B_z=\frac{\mu_0 I}{4 \pi r^2} d l \frac{R}{r} d B z = 4 π r 2 μ 0 I d l r R
Speed of Light in Terms of Permittivity and Permeability → \rightarrow → → \rightarrow → Magnetic Field due to Wire → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Magnetic Field due to Wire
d B z = μ 0 I R 4 π r 3 d l = μ 0 I R 4 π ( R 2 + z 2 ) 3 / 2 d l d B_z =\frac{\mu_0 I R}{4 \pi r^3}dl = \frac{\mu_0 I R}{4 \pi(R^2+z^2)^{3 / 2}} d l d B z = 4 π r 3 μ 0 I R d l = 4 π ( R 2 + z 2 ) 3/2 μ 0 I R d l
B z = μ o I R 4 π ( R 2 + z 2 ) 3 / 2 ∮ d l = μ 0 I R 4 π ( R 2 + z 2 ) 3 / 2 .2 π R B_z = \frac{\mu_o I R}{4 \pi (R^2+z^2)^{3/2}}\oint dl = \frac{\mu_0 I R}{4 \pi (R^2+z^2)^{3/2}}.2 \pi R B z = 4 π ( R 2 + z 2 ) 3/2 μ o I R ∮ d l = 4 π ( R 2 + z 2 ) 3/2 μ 0 I R .2 π R
= μ 0 I R 2 2 ( z 2 + R 2 ) 3 / 2 =\frac{\mu_0IR^2}{2(z^2+R^2)^{3/2}} = 2 ( z 2 + R 2 ) 3/2 μ 0 I R 2
Magnetic field on the Axis → \rightarrow → → \rightarrow → Magnetic Field due to Wire → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Magnetic Field at Axial Point
B ⃗ = μ 0 I R 2 2 ( z 2 + R 2 ) 3 / 2 k ^ \vec{B}=\frac{\mu_0 I R^2}{2(z^2+R^2)^{3 / 2}} \hat{k} B = 2 ( z 2 + R 2 ) 3/2 μ 0 I R 2 k ^
Magnetic Field due to Wire → \rightarrow → → \rightarrow → Magnetic Field at Axial Point → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Magnetic Field Centre of the Loop
At z = 0 (Centre of the loop)
B ⃗ = μ 0 I 2 R K ^ \vec{B}=\frac{\mu_0 I}{2 R} \hat{K} B = 2 R μ 0 I K ^
N - loop (closely around)
B ⃗ = μ 0 N I 2 R k ^ \vec{B}=\frac{\mu_0 N I}{2 R} \hat{k} B = 2 R μ 0 N I k ^
Magnetic Field due to Wire → \rightarrow → → \rightarrow → Magnetic Field Centre of the Loop → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Example
Magnetic Field at Axial Point → \rightarrow → → \rightarrow → Example → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Problem
Calculate the magnetude field at the centre of a circular are of wire of radius R carrying current I.
Magnetic Field Centre of the Loop → \rightarrow → → \rightarrow → Problem → \rightarrow → → \rightarrow →
Magnetostatics Introduction And Biot Savart Law L-5 Thank You
Example → \rightarrow → → \rightarrow → Thank You → \rightarrow → → \rightarrow →
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Magnetostatics Introduction And Biot Savart Law L-5 Magnetostatics Introduction and Biot Savart Law $\rightarrow$ $\rightarrow$ Magnetostatics Introduction and Biot Savart Law $\rightarrow$ Magnetostatics Introduction $\rightarrow$ Electric Field
