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
Define the term drift velocity.
What is its relation with relaxation time?
Write its (‘mobility’ of charge carriers) S.I. unit
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.
Why alloys like constantan and manganin are used for making standard resistors?
When electrons drift in a metal from lower to higher potential, does it mean that all the free electrons of the metal are moving in the same direction?
Define relaxation time of the free electrons drifting in a conductor. How is it related to the drift velocity of free electrons? Use this relation to deduce the expression for the electrical resistivity of the material.
Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation time.
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?
A current of 1.0 A exists in a copper wire of cross-section 1.0 mm2. Assuming one free electron per atom, calculate the drift speed of the free electrons in the wire. The density of copper is 9000 kg m–3.
Consider the following statements.
(A) Free-electron density is different in different metals.
(B) Free-electron density in a metal depends on temperature.
Seebeck Effect is caused _____________ .
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:
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 drift velocity of a free electron inside a conductor is ______
Is the momentum conserved when charge crosses a junction in an electric circuit? Why or why not?
The potential difference applied across a given conductor is doubled. How will this affect (i) the mobility of electrons and (ii) the current density in the 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.
