Physics assignment:
(1) Derive a relation for the electric potential at a certain point due to a point charge.
(2) Derive an expression for capacitance of a parallel plate capacitors.
(3) Derive an expression for Energy stored by the Capacitor.
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- 1.Electric potential of a point charge is V=kQ/r V = k Q / r . Electric potential is a scalar, and electric field is a vector. Addition of voltages as numbers gives the voltage due to a combination of point charges, whereas addition of individual fields as vectors gives the total electric field.
- ANSWER
- Let the two plates are kept parallel to each other separated be a distance d and cross-sectional area of each plate is A.
- Electric field by a single thin plate E
- ′
- =
- 2ϵ
- o
- σ
- Total electric field between the plates E=
- 2ϵ
- o
- σ
- +
- 2ϵ
- o
- σ
- Or E=
- ϵ
- o
- σ
- Or E=
- Aϵ
- o
- Q
- Potential difference between the plates V=Ed
- ⟹ V=
- Aϵ
- o
- Qd
- Capacitance C=
- V
- Q
- Thus we get capacitance of parallel plate capacitor C=
- d
- Aϵ
- o
- solution
- The energy stored in a capacitor can be expressed in three ways: Ecap=QV2=CV22=Q22C E cap = QV 2 = CV 2 2 = Q 2 2 C , where Q is the charge, V is the voltage, and C is the capacitance of the capacitor. The energy is in joules when the charge is in coulombs, voltage is in volts, and capacitance is in farads
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