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Two spherical...

Question

Two spherical shells are as shown in figure. Suppose r is the distance of a point from their common centre. Then, match the entries of column I with the entries of column II.
$\begin{matrix} C o l u m n - I & C o l u m n - I I (a) & Electric field for r < R_{1} & (p) & is constant for q_{2} and varying for q_{1} . (b) & Electric potential for r < R_{1} & (q) & is zero for q_{2} and varying for q_{1} (c) & Electric potential for R_{1} < r < R_{2} & (r) & is constant (d) & Electric field for R_{1} < r < R_{2} & (s) & zero \end{matrix}$

(a)

\to

(s); (b)

\to

(r); (c)

\to

(p); (d)

\to

(q);

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(a)

\to

(r); (b)

\to

(s); (c)

\to

(q); (d)

\to

(p);

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(a)

\to

(p); (b)

\to

(q); (c)

\to

(r); (d)

\to

(s);

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(a)

\to

(q); (b)

\to

(p); (c)

\to

(s); (d)

\to

(r);

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Solution

The correct option is A (a) $\to$ (s); (b) $\to$ (r); (c) $\to$ (p); (d) $\to$ (q);

$r < R_{1} E = 0 + 0 = 0 V = \frac{k q_{1}}{R_{1}} + \frac{k q_{2}}{R_{2}} =$ constant
$R_{1} < r < R_{2}$
$E = \frac{k q_{1}}{r^{2}} + 0$
$V = \frac{k q_{1}}{r} + \frac{k q_{2}}{R_{2}}$

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The correct option is A (a) → (s); (b) → (r); (c) → (p); (d) → (q); r<R1E=0+0=0V=kq1R1+kq2R2= constant R1<r<R2 E=kq1r2+0 V=kq1r+kq2R2

The correct option is A (a) $\to$ (s); (b) $\to$ (r); (c) $\to$ (p); (d) $\to$ (q);

$r < R_{1} E = 0 + 0 = 0 V = \frac{k q_{1}}{R_{1}} + \frac{k q_{2}}{R_{2}} =$ constant
$R_{1} < r < R_{2}$
$E = \frac{k q_{1}}{r^{2}} + 0$
$V = \frac{k q_{1}}{r} + \frac{k q_{2}}{R_{2}}$