Find the dimensions of magnetic permeability μ 0 , The relevant equations are : F = q E , F = q v B , B = μ 0 I 2 π r , p = q · r , M = I A , F = q 1 q 2 4 π ∈ 0 r 2 Where the other symbols F , q , v , I , r , A respectively represent force, charge, velocity, current, distance and area.

The magnetic permeability is given by B = μ 0 I 2 π r ⇒ μ 0 = 2 π r B I ∴ [ μ 0 ] = [ B ] [ r ] [ I ] [ ∵ 2 a n d π a r e d i m e n s i o n l e s s ] ⇒ [ μ 0 ] = [ M T - 2 A - ! ] [ L ] [ A ] [ ∵ [ B ] = [ M T - 2 A - 1 ] f r o m F = q v B ] ⇒ [ μ 0 ] = [ M L T - 2 A - 2 ] Therefore, dimension of magnetic permeability is [ M L T - 2 A - 2 ] .

Find the dimensions of magnetic permeability μ 0 , The relevant equations are : F = q E , F = q v B , B = μ 0 I 2 π r , p = q · r , M = I A , F = q 1 q 2 4 π ∈ 0 r 2 Where the other symbols F , q , v , I , r , A respectively represent force, charge, velocity, current, distance and area.

The magnetic permeability is given by B = μ 0 I 2 π r ⇒ μ 0 = 2 π r B I ∴ [ μ 0 ] = [ B ] [ r ] [ I ] [ ∵ 2 a n d π a r e d i m e n s i o n l e s s ] ⇒ [ μ 0 ] = [ M T - 2 A - ! ] [ L ] [ A ] [ ∵ [ B ] = [ M T - 2 A - 1 ] f r o m F = q v B ] ⇒ [ μ 0 ] = [ M L T - 2 A - 2 ] Therefore, dimension of magnetic permeability is [ M L T - 2 A - 2 ] .

Find the dimensions of electric permittivity ϵ 0 The relevant equations are : F = q E , F = q v B , B = μ 0 I 2 π r , p = q · r , M = I A , F = q 1 q 2 4 π ε 0 r 2 Where the other symbols F , q , v , I , r , A respectively represent force, charge, velocity, current, distance and area.

The electric permeability is given by F = q 1 q 2 4 π ε ∘ r 2 ⇒ ε ∘ = q 1 q 2 4 π r 2 F ∴ [ ε ∘ ] = [ A T ] [ A T ] L 2 M L T - 2 [ ∵ q = A t ] ⇒ [ ε ∘ ] = [ M - 1 L - 3 T 4 A 2 ] Therefore, dimensions of electric permittivity is M - 1 L - 3 T 4 A 2 .

Find the dimensions of electric dipole moment p , The relevant equations are : F = q E , F = q v B , B = μ 0 I 2 π r , p = q · r , M = I A , F = q 1 q 2 4 π ε 0 r 2 Where the other symbols F , q , v , I , r , A respectively represent force, charge, velocity, current, distance and area.

Dipole moment is given by p = q r where p is dipole moment q is charge and r is distance. ∴ [ p ] = [ q r ] ⇒ [ p ] = [ A T ] [ L ] [ ∵ [ q ] = [ A T ] ] ⇒ [ p ] = [ L T A ] Therefore, dimensions of dipole moment is L T A .

Find the dimensions of, magnetic dipole moment M , The relevant equations are : F = q E , F = q v B , B = μ 0 I 2 π r , p = q · r , M = I A and F = q 1 q 2 4 π ∈ 0 r 2 Where the other symbols F , q , v , I , r , A respectively represent force, charge, velocity, current, distance and area.

The magnetic moment is given by M = I A where M is magnetic moment , I is current and A is area. ∴ [ M ] = [ I ] [ A ] ⇒ [ M ] = [ A L 2 ] [ ∵ [ I ] = [ A ] a n d [ A ] = [ L 2 ] Therefore, the dimensions of magnetic moment are L 2 A .

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11th West Bengal Board

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Find the dimensions of magnetic permeability $(μ_{0})$ , The relevant equations are :

$F = q E, F = q v B, B = \frac{μ_{0} I}{2 π r}, p = q \cdot r, M = I A$ , $F = \frac{q_{1} q_{2}}{4 π \in_{0} r^{2}}$

Where the other symbols $F, q, v, I, r, A$ respectively represent force, charge, velocity, current, distance and area.

Important Questions on Dimensions of Physical Quantities and Dimensional Analysis

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IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 2

Find the dimensions of electric permittivity $(ϵ_{0})$ The relevant equations are :

$F = q E, F = q v B, B = \frac{μ_{0} I}{2 π r}, p = q \cdot r, M = I A$ , $F = \frac{q_{1} q_{2}}{4 π ε_{0} r^{2}}$

Where the other symbols $F, q, v, I, r, A$ respectively represent force, charge, velocity, current, distance and area.

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 2

Find the dimensions of electric dipole moment $(p)$ , The relevant equations are :

$F = q E, F = q v B, B = \frac{μ_{0} I}{2 π r}, p = q \cdot r, M = I A$ , $F = \frac{q_{1} q_{2}}{4 π ε_{0} r^{2}}$

Where the other symbols $F, q, v, I, r, A$ respectively represent force, charge, velocity, current, distance and area.

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11th West Bengal Board

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 2

Find the dimensions of, magnetic dipole moment $(M)$ , The relevant equations are :

$F = q E, F = q v B, B = \frac{μ_{0} I}{2 π r}, p = q \cdot r, M = I A$ and

$F = \frac{q_{1} q_{2}}{4 π \in_{0} r^{2}}$

Where the other symbols $F, q, v, I, r, A$ respectively represent force, charge, velocity, current, distance and area.

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11th West Bengal Board

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 3

Find the dimensions of Planck's constant

h

from the equation

E = h v

, where

E

is energy and

v

is frequency.

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 4

If we take force, length and time to be the fundamental quantities then find the dimensions of density

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 4

If we take force, length and time to be the fundamental quantities then find the dimensions of pressure

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 4

If we take force, length and time to be the fundamental quantities then find the dimensions of momentum.

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 4

If we take force, length and time to be the fundamental quantities, then find the dimensions of energy.

Find the dimensions of magnetic permeability μ0, The relevant equations are : F=qE, F=qvB, B=μ0I2πr, p=q·r, M=IA, F=q1q24π∈0r2 Where the other symbols F, q, v, I, r, A respectively represent force, charge, velocity, current, distance and area.

Important Questions on Dimensions of Physical Quantities and Dimensional Analysis

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