Figure shows three spherical and equipotential surfaces $A$ , $B$ and $C$ around a point charge $q$ . The potential difference $V_{A} - V_{B} = V_{B} - V_{C}$ . If $t_{1}$ and $t_{2}$ be the distances between them, then :

$t_{1} = t_{2}$
$t_{1} \leq t_{2}$
$t_{1} < t_{2}$
$t_{1} > t_{2}$

Question

Figure shows three spherical and equipotential surfaces $A$ , $B$ and $C$ around a point charge $q$ . The potential difference $V_{A} - V_{B} = V_{B} - V_{C}$ . If $t_{1}$ and $t_{2}$ be the distances between them, then :

$t_{1} = t_{2}$
$t_{1} \leq t_{2}$
$t_{1} < t_{2}$
$t_{1} > t_{2}$

Toppr Admin · Accepted Answer

The potential around a point charge is V-r-q4-x3C0-x3F5-0rLet a-b-c be the radii of A-B-C respectively-Thus- t1-b-x2212-a and t2-c-x2212-bVA-x2212-VB-q4-x3C0-x3F5-0a-x2212-q4-x3C0-x3F5-0b-q-xA0-t14-x3C0-x3F5-0abVB-x2212-VC-q4-x3C0-x3F5-0b-x2212-q4-x3C0-x3F5-0c-q-xA0-t24-x3C0-x3F5-0bcBut- VA-x2212-VB-VB-x2212-VC-x21D2-VA-x2212-VBVB-x2212-VC-1-x21D2-t1ab-xD7-bct2-1-x21D2-t1t2-acAs a-lt-c- we have t1-lt-t2

Figure shows three spherical and equipotential surfaces A, B and C around a point charge q. The potential difference VA−VB=VB−VC. If t1 and t2 be the distances between them, then :t1=t2t1≤t2t1<t2t1>t2

The potential around a point charge is V(r)=q4πϵ0rLet a,b,c be the radii of A,B,C respectively.Thus, t1=b−a and t2=c−bVA−VB=q4πϵ0a−q4πϵ0b=q t14πϵ0abVB−VC=q4πϵ0b−q4πϵ0c=q t24πϵ0bcBut, VA−VB=VB−VC⇒VA−VBVB−VC=1⇒t1ab×bct2=1⇒t1t2=acAs a<c, we have t1<t2

Figure shows three spherical and equipotential surfaces $A$ , $B$ and $C$ around a point charge $q$ . The potential difference $V_{A} - V_{B} = V_{B} - V_{C}$ . If $t_{1}$ and $t_{2}$ be the distances between them, then :

$t_{1} = t_{2}$
$t_{1} \leq t_{2}$
$t_{1} < t_{2}$
$t_{1} > t_{2}$