A point charge of charge q and mass m is placed at rest at point X at distance r from a short electric dipole. The initial acceleration of charge a=(k ⋅ q ⋅ p/2 m r3) n, where k=(1/4 π ε0). Then n is (short electric dipole)

Question

A point charge of charge q and mass m is placed at rest at point X at distance r from a short electric dipole. The initial acceleration of charge a=(k ⋅ q ⋅ p/2 m r3) n, where k=(1/4 π ε0). Then n is (short electric dipole) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

a=(F/m)=(E q/m)=[(1/4 π ε0) (P √3 cos 2 60°+1/r3)] (q/m) =(q/m)[(1/4 π ε0) (P √3((1/2))2+1/r3)] =(√7/2)((1/4 π ε0)) (q P/m r3) text .

Q. A point charge of charge $q$ and mass $m$ is placed at rest at point $X$ at distance $r$ from a short electric dipole. The initial acceleration of charge $a = \frac{k \cdot q \cdot p}{2 m r ^{3}} n$ , where $k = \frac{1}{4 π ε _{0}}$ . Then $n$ is (short electric dipole)

$a = \frac{F}{m} = \frac{Eq}{m} = [\frac{1}{4 π ε _{0}} \frac{P 3 c o s ^{2} 6 0 ^{\circ} + 1}{r ^{3}}] \frac{q}{m}$
$= \frac{q}{m} [\frac{1}{4 π ε _{0}} \frac{P 3 ( \frac{1}{2} ) ^{2} + 1}{r ^{3}}]$
$= \frac{7}{2} (\frac{1}{4 π ε _{0}}) \frac{qP}{m r ^{3}} .$

Q. A point charge of charge q and mass m is placed at rest at point X at distance r from a short electric dipole. The initial acceleration of charge a=2mr3k⋅q⋅p​n, where k=4πε0​1​. Then n is (short electric dipole)

a=mF​=mEq​=[4πε0​1​r3P3cos260∘+1​​]mq​ =mq​[4πε0​1​r3P3(21​)2+1​​] =27​​(4πε0​1​)mr3qP​.

Q. A point charge of charge $q$ and mass $m$ is placed at rest at point $X$ at distance $r$ from a short electric dipole. The initial acceleration of charge $a = \frac{k \cdot q \cdot p}{2 m r ^{3}} n$ , where $k = \frac{1}{4 π ε _{0}}$ . Then $n$ is (short electric dipole)

$a = \frac{F}{m} = \frac{Eq}{m} = [\frac{1}{4 π ε _{0}} \frac{P 3 c o s ^{2} 6 0 ^{\circ} + 1}{r ^{3}}] \frac{q}{m}$
$= \frac{q}{m} [\frac{1}{4 π ε _{0}} \frac{P 3 ( \frac{1}{2} ) ^{2} + 1}{r ^{3}}]$
$= \frac{7}{2} (\frac{1}{4 π ε _{0}}) \frac{qP}{m r ^{3}} .$