Question

1) Two charges of magnitude 5nC & -2nC are placed at points ( 2cm , 0 , 0 ) & ( 20cm , 0 , 0 ) in a region of space, where there is no external field.. Find electrostatic potential energy of the system.

2) An emf of 96 mV is induced in the windings of a coil when the current in the nearby coil is increased at the rate of 1.20 A/s. What is the mutual inductance of the two coils?​

Answer 1

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1 .Two charges of magnitude 5nC and - 2nC are placed at 2cm and 20cm from the origin respectively.

We know that,

$\sf U = \dfrac{1}{4 \pi \epsilon_o} \times \dfrac{q_1q_2}{\Delta{r}}$

Substituting the values,

$\begin{gathered} \longrightarrow \sf U = 9 \times {10}^{9} \times \dfrac{5 \times {10}^{ - 9} \times - 2 \times {10}^{ - 9} }{20 \times {10}^{ - 2} - 2 \times {10}^{ - 2} } \\ \\ \longrightarrow \sf U = - \dfrac{9 \times 10 \times {10}^{ - 9} }{18 \times {10}^{ - 2} } \\ \\ \longrightarrow \ \boxed{ \boxed{\sf U = - 0.5 \times {10}^{ - 6} J}}\end{gathered}$

2. Given Information,

EMF = 96mV

Rate of change of current w.r.t t = 1.20 A/s

Since,

$\sf E = L \dfrac{dl}{dt}$

Substituting the values,

$\begin{gathered} \longrightarrow \sf 96 \times 10 {}^{ - 3} = L \times 1.2 \\ \\ \longrightarrow \boxed{ \boxed{\sf \: L = 8 \times {10}^{ - 2} H}}\end{gathered}$

Answer 2

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$\sf U = \dfrac{1}{4 \pi \epsilon_o} \times \dfrac{q_1q_2}{\Delta{r}} \\ \bf Substituting \: the \: values, \\ \begin{gathered}\begin{gathered} \longrightarrow \sf U = 9 \times {10}^{9} \times \dfrac{5 \times {10}^{ - 9} \times - 2 \times {10}^{ - 9} }{20 \times {10}^{ - 2} - 2 \times {10}^{ - 2} } \\ \\ \longrightarrow \sf U = - \dfrac{9 \times 10 \times {10}^{ - 9} }{18 \times {10}^{ - 2} } \\ \\ \longrightarrow \ \boxed{ \boxed{\sf U = - 0.5 \times {10}^{ - 6} J}}\end{gathered} \end{gathered} \\ \sf E = L \dfrac{dl}{dt} \\ \bf \: Substituting \: the \: values, \\ \begin{gathered}\begin{gathered} \longrightarrow \sf 96 \times 10 {}^{ - 3} = L \times 1.2 \\ \\ \longrightarrow \boxed{ \boxed{\sf \: L = 8 \times {10}^{ - 2} H}}\end{gathered}\end{gathered}$