The electric potential at a point in free space due to a charge Q coulomb is Q × 10^11 volts. The electric field at that point is ?

The electric potential at a point in free space due to a charge Q coulomb is Q × 10^11 volts. The electric field at that point is ?


(a) \( 4\pi \varepsilon_0 Q \times 10^{22} \, \text{volt/m} \)

(b) \( 12\pi \varepsilon_0 Q \times 10^{20} \, \text{volt/m} \)

(c) \( 4\pi \varepsilon_0 Q \times 10^{20} \, \text{volt/m} \)

(d) \( 12\pi \varepsilon_0 Q \times 10^{22} \, \text{volt/m} \)


Answer :  (a) \( 4\pi \varepsilon_0 Q \times 10^{22} \, \text{volt/m} \)


\[ E = \dfrac{kQ}{r^2} \]


\( V = \dfrac{kQ}{r} = Q \times 10^{11} \) \( \Rightarrow \dfrac{Q}{r} = 4\pi \varepsilon_0 Q \times 10^{11} \\ \)


\( E = \dfrac{Q \times 10^{11}}{r} \\ \)


\( = 4\pi \varepsilon_0 Q \times 10^{11} \times 10^{11} \\ \)


\( = 4\pi \varepsilon_0 Q \times 10^{22} \)





No comments:

Post a Comment

Please provide your valuable feedback. Students, Parents, Teachers.