The magnetic force depends on $v$,which depends on the inertial frame of reference. Does the magnetic force differ from one inertial frame to another? Is it reasonable that the net acceleration has a different value in different frames of reference?
(N/A) The magnetic force is given by $\vec{F}_m = q(\vec{v} \times \vec{B})$. Since the velocity $\vec{v}$ of a charged particle depends on the inertial frame of reference,the magnetic force experienced by the particle also depends on the frame of reference.
However,the total force (Lorentz force) is $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$. When we change the frame of reference,the electric field $\vec{E}$ and magnetic field $\vec{B}$ transform such that the total force $\vec{F}$ remains consistent with the laws of physics in that frame.
Regarding the net acceleration,according to Newton's second law,$\vec{a} = \vec{F}/m$. Since the force $\vec{F}$ is frame-dependent,the acceleration $\vec{a}$ can indeed be different in different inertial frames. This is consistent with the principle of relativity,as long as the laws of physics (like Maxwell's equations) are invariant across these frames.
However,the total force (Lorentz force) is $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$. When we change the frame of reference,the electric field $\vec{E}$ and magnetic field $\vec{B}$ transform such that the total force $\vec{F}$ remains consistent with the laws of physics in that frame.
Regarding the net acceleration,according to Newton's second law,$\vec{a} = \vec{F}/m$. Since the force $\vec{F}$ is frame-dependent,the acceleration $\vec{a}$ can indeed be different in different inertial frames. This is consistent with the principle of relativity,as long as the laws of physics (like Maxwell's equations) are invariant across these frames.
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In electromagnetic theory, electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related. In the questions below, $[E]$ and $[B]$ stand for dimensions of electric and magnetic fields respectively, while $[\varepsilon_0]$ and $[\mu_0]$ stand for dimensions of the permittivity and permeability of free space respectively. $L$ and $T$ are dimensions of length and time respectively. All quantities are in $SI$ units.
$(1)$ The relation between $[E]$ and $[B]$ is:
$(A)$ $[E]=[B][L][T]^{-1}$
$(B)$ $[E]=[B][L][T]$
$(C)$ $[E]=[B][L]^{-1}[T]$
$(D)$ $[E]=[B][L]^{-1}[T]^{-1}$
$(2)$ The relation between $[\varepsilon_0]$ and $[\mu_0]$ is:
$(A)$ $[\mu_0]=[\varepsilon_0][L]^2[T]^{-2}$
$(B)$ $[\mu_0]=[\varepsilon_0]^{-1}[L]^{-2}[T]^2$
$(C)$ $[\mu_0]=[\varepsilon_0][L]^{-2}[T]^2$
$(D)$ $[\mu_0]=[\varepsilon_0]^{-1}[L]^2[T]^{-2}$
Select the correct options for $(1)$ and $(2)$.
$(1)$ The relation between $[E]$ and $[B]$ is:
$(A)$ $[E]=[B][L][T]^{-1}$
$(B)$ $[E]=[B][L][T]$
$(C)$ $[E]=[B][L]^{-1}[T]$
$(D)$ $[E]=[B][L]^{-1}[T]^{-1}$
$(2)$ The relation between $[\varepsilon_0]$ and $[\mu_0]$ is:
$(A)$ $[\mu_0]=[\varepsilon_0][L]^2[T]^{-2}$
$(B)$ $[\mu_0]=[\varepsilon_0]^{-1}[L]^{-2}[T]^2$
$(C)$ $[\mu_0]=[\varepsilon_0][L]^{-2}[T]^2$
$(D)$ $[\mu_0]=[\varepsilon_0]^{-1}[L]^2[T]^{-2}$
Select the correct options for $(1)$ and $(2)$.
DifficultIIT 2018
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