Figure shows a circular area of radius R where a uniform magnetic field vecB is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?

Question

Figure shows a circular area of radius R where a uniform magnetic field vecB is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

B = B 0 t r > R φ barε ⋅ de =( d φ/ dt ) ⇒ ε(2 π r )= B π r 2

e propto r r > R ε(2 π r )= B π R 2 ε propto (1/r)

Q. Figure shows a circular area of radius R where a uniform magnetic field $B$ is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?

$B = B_{0} t$
$r > R$
$ϕ \overset{ε}{ˉ} \cdot d e = \frac{d ϕ}{d t}$
$\Rightarrow ε (2 π r) = B π r^{2}$

$e \propto r$
$r > R$
$ε (2 π r) = B π R^{2}$
$ε \propto \frac{1}{r}$

Q. Figure shows a circular area of radius R where a uniform magnetic field B is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?

B=B0​t r>R ϕεˉ⋅de=dtdϕ​ ⇒ε(2πr)=Bπr2 e∝r r>R ε(2πr)=BπR2 ε∝r1​

Q. Figure shows a circular area of radius R where a uniform magnetic field $B$ is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?

$B = B_{0} t$
$r > R$
$ϕ \overset{ε}{ˉ} \cdot d e = \frac{d ϕ}{d t}$
$\Rightarrow ε (2 π r) = B π r^{2}$

$e \propto r$
$r > R$
$ε (2 π r) = B π R^{2}$
$ε \propto \frac{1}{r}$