Question

Match Column I with Column II:

Column I		Column II
A	Dielectric ring uniformly charged.	P	Time independent electrostatic field out of system.
B	Dielectric ring uniformly charged rotating with angular velocity $\omega$.	Q	Magnetic field.
C	Constant current in ring $i_{0}$.	R	Induced electric field.
D	$i =i_{0} \cos \omega t$	S	Magnetic moment.

• A. $( A ) \rightarrow( P ) ;( B ) \rightarrow( Q ),( S ) ;( C ) \rightarrow( Q ),( S ) ;( D ) \rightarrow( P )$
• B. $( A ) \rightarrow( P ) ;( B ) \rightarrow( Q ),( S ) ;( C ) \rightarrow( Q ),( S ) ;( D ) \rightarrow( Q ),( S )$
• C. $( A ) \rightarrow( P ) ;( B ) \rightarrow( Q ),( S ) ;( C ) \rightarrow( Q ),( S ) ;( D ) \rightarrow( Q ),( R )(S)$
• D. $( A ) \rightarrow( P ) ;( B ) \rightarrow( Q ),( S ) ;( C ) \rightarrow( Q ),( S ) ;( D ) \rightarrow( R ),( S )$

Answer 1

Answer: (C)

$( A ) \rightarrow( P )$
$E =\frac{k q x}{\left(a^{2}+x^{2}\right)^{\frac{3}{2}}}$

(B) $\rightarrow(Q),(S)$
A rotating (accelerated) charge creates a magnetic field. There is also a magnetic movement, namely, $\vec{m}=i \vec{A}$ associated with it.
$( C ) \rightarrow( Q ),( S )$

$\frac{\mu_{0} i a^{2}}{2\left(a^{2}+x^{2}\right)^{\frac{3}{2}}} $
$\vec{m}=i_{0} \vec{A} $
$( D ) \rightarrow( Q ),( R ),( S )$
Time-varying current creates a time-varying field. Hence, the magnetic flux also varies with time, which creates induced emf (induced $\vec{E}$ ) in accordance with Faraday's law.