A small sphere with mass 1-2 g hangs by a thread between two parallel vertical plates 5 cm apart- The plates are insulating and have uniform surface charge densities - and - The charge on the sphere is q-9 - 10-6 C- What potential difference in V between the plates will cause the thread to assume an angle of 37- with the vertical as shown in figure-

According to the question FBD can be given as nbsp; From the FBD we can say that tan37^∘=F_E/mg ⇒3/4=qE/mg ⇒ E=3mg/4q To find out potential we multiply both ...

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Standard XII

Physics

Potential Gradient and Relation between Electric Field and Potential

A small spher...

Question

A small sphere with mass $1.2 g$ hangs by a thread between two parallel vertical plates $5 c m$ apart. The plates are insulating and have uniform surface charge densities $+ δ$ and $- δ$ . The charge on the sphere is $q = 9 \times 10^{- 6} C$ . What potential difference (in V) between the plates will cause the thread to assume an angle of $37^{\circ}$ with the vertical as shown in figure?

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Solution

According to the question FBD can be given as

From the FBD we can say that
$tan 37^{\circ} = \frac{F_{E}}{m g} \Rightarrow \frac{3}{4} = \frac{q E}{m g} \Rightarrow E = \frac{3 m g}{4 q}$
To find out potential we multiply both sides with $^{'} d^{'}$ which is the distance between the plates
$\Rightarrow E . d = \frac{3 m g d}{4 q}$
Putting the values
$V = \frac{3 \times 1.2 \times 10^{- 3} \times 10 \times 5 \times 10^{- 2}}{4 \times 9 \times 10 - 6} = 50 V$

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According to the question FBD can be given as From the FBD we can say that tan37∘=FEmg⇒34=qEmg⇒E=3mg4q To find out potential we multiply both sides with ′d′ which is the distance between the plates ⇒E.d=3mgd4q Putting the values V=3×1.2×10−3×10×5×10−24×9×10−6=50 V