Advertisements
Advertisements
Question
The electrostatic potential is given as a function of x in figure (a) and (b). Calculate the corresponding electric fields in regions A, B, C and D. Plot the electric field as a function of x for figure (b).
Advertisements
Solution
Figure a:
`vec"E" = - "dv"/"dx" hat"i"`
From 0 to 0.2 m,
`"E"_"x" = "dv"/"dx" = 3/0.2 = 30/2 = 15`Vm-1 (region A)
`"E"_"x" = "dv"/"dx"` = 0
Since the potential is constant (region B)
`"E"_"x" = "dv"/"dx" = (-2)/0.2 = (-20)/2` = - 10 Vm-1 (region c)
`"E"_"x" = "dv"/"dx" = 6/0.2 = 60/2` = 30 Vm-1 (region d)
Figure b:
`"E"_"x" = "dv"/"dx"` = - 30 Vm-1 (region 0-1 cm)
`"E"_"x" = "dv"/"dx"` = 30 Vm-1 (region 1-2 cm)
`"E"_"x" = "dv"/"dx"` = 0 (region 2-3 cm)
`"E"_"x" = "dv"/"dx"` = 30 Vm-1 (region 3-4 cm)
`"E"_"x" = "dv"/"dx"` = - 30 Vm-1 (region 4-5 cm)
APPEARS IN
RELATED QUESTIONS
Rank the electrostatic potential energies for the given system of charges in increasing order.
What is an equipotential surface?
Define ‘electrostatic potential energy’.
What is meant by electrostatic energy density?
Derive an expression for electrostatic potential due to a point charge.
Derive an expression for electrostatic potential due to an electric dipole.
Obtain an expression for potential energy due to a collection of three point charges which are separated by finite distances.
Suppose a charge +q on Earth’s surface and another +q charge is placed on the surface of the Moon,
- Calculate the value of q required to balance the gravitational attraction between Earth and Moon
- Suppose the distance between the Moon and Earth is halved, would the charge q change?
(Take mE = 5.9 x 1024 kg, mM = 7.348 x 1022 kg)
Draw the free body diagram for the following charges as shown in the following figure.
A spark plug in a bike or a car is used to ignite the air-fuel mixture in the engine. It consists of two electrodes separated by a gap of around 0.6 mm gap as shown in the figure.
To create the spark, an electric field of magnitude 3 x 106Vm-1 is required,
- What potential difference must be applied to produce the spark?
- If the gap is increased, does the potential difference increase, decrease or remains the same?
- Find the potential difference if the gap is 1 mm.
