Question : Across a metallic conductor of non-uniform cross-section, a constant potential difference is applied. The quantity which remains constant along the conductor is
a) current
b) drift velocity
c) electric field
d) current density
Solution :
In a metallic conductor of non-uniform cross-section, the area keep on changing i.e. the thickness of wire is keep on changing.
In a metallic conductor of non-uniform cross-section, the area keep on changing i.e. the thickness of wire is keep on changing.
(a) We know,
I =dq/dt
As per the law of conservation of charges, total charge entering per second through one end of the wire is equal to the total change leaving per second through the other end of the wire.
Hence, the current through the wire of uniform cross section will remain constant.
I =dq/dt
As per the law of conservation of charges, total charge entering per second through one end of the wire is equal to the total change leaving per second through the other end of the wire.
Hence, the current through the wire of uniform cross section will remain constant.
(b) As per the relation
I=neVdA
Vd=I/neA
Clearly, drift velocity depends on the Area of the cross section of wire hence, it will not remain constant.
(c) Electric Field
We know,
j = σE
I/A=σE
E=I/σA
Clearly, Electric Field also depends on Area of cross section of wire (A). Hence, electric field is also not constant throughout the wire.
(d) Current Density
j=I/A
Clearly, the current density also depends on area of cross section of wire. Hence, current density (j) is also not constant throughout the wire.
I=neVdA
Vd=I/neA
Clearly, drift velocity depends on the Area of the cross section of wire hence, it will not remain constant.
(c) Electric Field
We know,
j = σE
I/A=σE
E=I/σA
Clearly, Electric Field also depends on Area of cross section of wire (A). Hence, electric field is also not constant throughout the wire.
(d) Current Density
j=I/A
Clearly, the current density also depends on area of cross section of wire. Hence, current density (j) is also not constant throughout the wire.
Hence, the only quantity which remains constant throughout the wire having non uniform cross section is electric current.
Hence, (a) current would be the only correct option.
