Advertisements
Advertisements
Question
Electrons are emitted by a hot filament and are accelerated by an electric field, as shown in the figure. The two stops at the left ensure that the electron beam has a uniform cross-section.
Options
The speed of the electrons is more at B than at A
The electric current is from left to right
The magnitude of the current is larger at B than at A
The current density is more at B than at A
Advertisements
Solution
The speed of the electrons is more at B than at A
Let the potentials at A and B be VA and VB.
As potential,
\[E = - \frac{dV}{dr}\]
potential increases in the direction opposite to the direction of the electric field.
Thus, VA < VB
Potential energy of the electrons at points A and B:-
UA = -eVA
UB = -eVB
Thus, UA > UB
Let the kinetic energy of an electron at points A and B be KA and KB respectively.
Applying the principle of conservation of mechanical energy, we get:-
UA + KA = UB + KB
As, UA > UB,
KA < KB
Therefore, the speed of the electrons is more at B than at A.
APPEARS IN
RELATED QUESTIONS
Derive an expression for drift velocity of free electrons.
What is its relation with relaxation time?
Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0 × 10−7 m2 carrying a current of 1.5 A. Assume the density of conduction electrons to be 9 × 1028 m−3
How does drift velocity of electrons in a metallic conductor vary with increase in temperature? Explain.
(a) drift speed
(b) current density
(c) electric current
(d) electric field
Explain the term ‘drift velocity’ of electrons in conductor. Hence obtain the expression for the current through a conductor in terms of ‘drift velocity’.
When a current is established in a wire, the free electrons drift in the direction opposite to the current. Does the number of free electrons in the wire continuously decrease?
Consider a wire of length 4 m and cross-sectional area 1 mm2 carrying a current of 2 A. If each cubic metre of the material contains 1029 free electrons, find the average time taken by an electron to cross the length of the wire.
When a current I is set up in a wire of radius r, the drift velocity is vd· If the same current is set up through a wire of radius 2 r, the drift velocity will be:
At room temperature, copper has free electron density of 8.4 × 1028 per m3. The copper conductor has a cross-section of l0−6 m2 and carries a current of 5.4 A. The electron drift velocity in copper is:
Metals are good conductor of heat than insulator because
Amount of charge in coulomb required to deposit one gram equivalent of substance by electrolysis is:-
An electric bulb.is rated 220 v and 100 watt power consumed by it when operated on 'no volt is:-
The identical conductors maintained at same temperature are given potential difference in the ratio 1 : 2. Then the ratio of their drift velocities is ______.
The relaxation time τ is nearly independent of applied E field whereas it changes significantly with temperature T. First fact is (in part) responsible for Ohm’s law whereas the second fact leads to variation of ρ with temperature. Elaborate why?
Explain how free electrons in a metal at constant temperature attain an average velocity under the action of an electric field. Hence, obtain an expression for it.
A potential difference (V) is applied across a conductor of length 'L' and cross-sectional area 'A'.
How will the drift velocity of electrons and the current density be affected if another identical conductor of the same material were connected in series with the first conductor? Justify your answers.
Two conductors, made of the same material have equal lengths but different cross-sectional areas A1 and A2 (A1 > A2). They are connected in parallel across a cell. Show that the drift velocities of electrons in two conductors are equal.
