# Current Density Vector

## Trending Questions

**Q.**A copper wire of length 10 m and radius (10−2/√π)m has electrical resistance of 10 Ω. The current density in the wire for an electric field strength of 10( V/m) is:

- 106 A/m2
- 105 A/m2
- 10−5 A/m2
- 104 A/m2

**Q.**(a) Define the term 'conductivity' of a metallic wire. Write its SI unit.

(b) Using the concept of free electrons in a conductor, derive the expression for the conductivity of a wire in terms of number density and relaxation time. Hence obtain the relation between current density and the applied electric field E.

**Q.**The current density across a cylindrical conductor of radius R varies according to the equation J=J0(1−rR), where r is the distance from the axis. Thus, the current density is a maximum J0 at the axis r=0 and decreases linearly to zero at the surface r=R. Calculate the current, I in terms of J0 if the conductor's cross sectional area is A=πR2.

- I=J0A3
- I=J0A6
- I=J0A9
- I=J0A12

**Q.**

An electron of mass $m$ and magnitude of charge$\left|e\right|$ initially at rest gets accelerated by a constant electric field $E$. The rate of change of de-Broglie wavelength of this electron at time $t$ ignoring relativistic effects is

$-\frac{\left|e\right|Et}{h}$

$-\frac{h}{\left|e\right|E\sqrt{t}}$

$-\frac{h}{\left|e\right|E{t}^{2}}$

$-\frac{2h{t}^{2}}{\left|e\right|E}$

**Q.**A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m2. At every point, the direction of current density is at an angle of 60∘, with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is :

Resistivity of magnesium is 44×10–8 Ω-m.

- 11×10−7 V/m
- 11×10−3 V/m
- 11×10−5 V/m
- 11×10−2 V/m

**Q.**

A potential difference $\mathrm{V}$ is applied across a conductor of length $\u2018\mathrm{l}\u2019$. How is the drift velocity affected when $\mathrm{V}$ is doubled and $\u2018\mathrm{l}\u2019$ is halved?

**Q.**

Let I = current through a conductor, R = its resistance and V = potential difference across its ends. According to Ohm's law, product of two of these quantities equals the third. Obtain Ohm's law from dimensional analysis. Dimensional formulae for R and V are ML2I−2T−3 and ML2T−3I−1 respectively.

**Q.**The current density across a cylindrical conductor of radius R varies in magnitude according to the equation J=J0(1−rR) where r is the distance from the central axis. Thus, the current density is maximum J0 at the axis (r=0) and decreases linearly to zero at the surface (r=R). The current in terms of J0 and conductor's cross-sectional area A is :-

- J0A3
- J0A6
- J0A2
- J0A5

**Q.**A non uniform electric field is given by the expression \overrightarrow E =ay\overrightarrow i +bz \overrightarrow j + cx\overrightarrow{} , where a , b , c are cons†an ts . Determine the electric flux through a rec†an gular surface in the xy plane , extending from x=0 to x= w and from y=0 to y=h

**Q.**An electric current of 8 Amperes is measured across an area of 50cm2, then current density in this area is:

- Must be greater than or equal to 1600A/m2
- Must be less than or equal to 1600A/m2
- Cannot say
- Must be 1600A/m2

**Q.**The variation of current and voltage in a conductor has been shown in figure. The conductance of the conductor is (Give your answer in Ω−1).

- 12
- 15
- 13
- 14

**Q.**A copper wire of length 1m and radius 1mm is joined in series with an iron wire of length 2m and radius 3mm and a current is passed through the wire. The ratio of current densities in the copper and iron wire is

- 18 : 1
- 9 : 1
- 6 : 1
- 2 : 3

**Q.**

Does de-Broglie wavelength depend on charge?

**Q.**A Conductor with rectangular cross-section has dimensions (a×2a×4a) as shown in figure. Resistance across AB is x, across CD is y and across EF is z. Then

- x=y=z
- x>y>z
- y>z>x
- x>z>y

**Q.**

why is it so that when the diametre of a conductor is doubled, then drift velocity of electrons inside it will not change

**Q.**The electric current in an X- ray tube (from the target to the filament) operating at 40 kV is 10 mA. Assume that on an average, 1% of the total kinetic energy of the electrons hitting the target are converted into X−rays. The total power (in W) emitted as X-rays is

**Q.**

A $150m$ long metal wire connects points $A$ and $B$. The electric potential at point $B$ is $50V$ less than that at point $A$. If the conductivity of the metal is $60\times {10}^{6}mho/m$ then the magnitude of the current density in the wire is equal to?

**Q.**

A long straight metal rod has a very long hole of radius ′a′ drilled parallel to the rod axis as shown in the figure. If the rod carries a current ′I′. Find the magnetic induction on the axis of the hole, where$\mathrm{OC}=\mathrm{c}$:

$\frac{{\mathrm{\mu}}_{0}\mathrm{Ic}}{\mathrm{\pi}\left({\mathrm{b}}^{2}-{\mathrm{c}}^{2}\right)}$

$\frac{{\mathrm{\mu}}_{0}\mathrm{Ic}}{2\mathrm{\pi}\left({\mathrm{b}}^{2}-{\mathrm{c}}^{2}\right)}$

$\frac{{\mathrm{\mu}}_{0}\mathrm{I}\left({\mathrm{b}}^{2}-{\mathrm{c}}^{2}\right)}{2\mathrm{\pi c}}$

$\frac{{\mathrm{\mu}}_{0}\mathrm{Ic}}{2{\mathrm{\pi a}}^{2}{\mathrm{b}}^{2}}$

**Q.**A long straight cylindrical region of radius a carries a current along its length. The current density (J) varies from the axis to the edge of the cylindrical region according to J=J0(1−ra) , where r is distance from the axis (0≤r≤a). Choose the correct answer (s) among the following.

- Mean density ¯J=J03
- At r=0 ; B=0
- At r=a ; B=μ0J0a6
- The B−r graph is parabolic with maxima at distance r=a2

**Q.**Find the current flowing through a copper wire of length 0.2 m, area of cross-section 1 mm2, when connected to a battery of 4 V. Given that electron mobility =4.5×10−6 m2Vs and charge on electron =1.6×10−19 C. The number density of electron in copper is 8.5×1028 m−3.

- 1.22 A
- 2.12 A
- 4.52 A
- 4.68 A

**Q.**

A wire of 10−3cm2 cross sectional area carries a current of 0.25 A, then current density is

1.5×10

^{6}Am^{-2}2.5×10

^{6}Am^{-2}3.5×10

^{6}Am^{-2}4.5×10

^{6}Am^{-2}

**Q.**{ †ext { An electric dipole of length } 10 cm †ext { having charges } + 6 × 10 ^ { - 3 } C †ext { and } - 6 × 10 ^ { - 3 } C †ext { , placed at } } { 30 ^ { ° } †ext { with respect to a uniform electric field experiences a torque of magnitude } 6 \sqrt { 3 } Nm †ext { . } } { †ext { Calculate the magnitude of electric field. }

**Q.**For a metallic conductor, what is the relation between current density (j), conductivity (σ) and electric field Intensity E?

**Q.**

When will the conductivity become equal to the molar conductivity?

**Q.**At some higher altitude, density of free electrons is around

1012 per cubic meter and due to low density of air the mean path of an electron is about 0.1m. If the mean speed of electrons is 105 m/s, then the conductivity of atmosphere is

(answer upto 2 decimal points)

**Q.**I apply an electric field of 105N/C on a conductor of cross section 4mm2 and I get a current of 1A. If I want to change the current to 0.3A, what is the electric field I need to apply?

- 5×104N/C
- 4×104N/C
- 3×104N/C
- 2×104N/C

**Q.**The current density across a cylindrical conductor of radius R varies according to the equation J=J0(1−rR), where r is the distance from the axis. Thus, the current density is a maximum J0 at the axis r=0 and decreases linearly to zero at the surface r=R. Calculate the current, I in terms of J0 if the conductor's cross sectional area is A=πR2.

- I=J0A12
- I=J0A9
- I=J0A6
- I=J0A3

**Q.**Explain the term 'drift velocity' of electrons in a conductor. Hence obtain the expression for the current through a conductor in terms of 'drift velocity'.

**Q.**A wire of resistance 12 Ω/m is bent to form a complete circle of radius 10 cm. The resistance between its two diametrically opposite points, A and B as shown in the figure is -

- 6 Ω
- 0.6π Ω
- 3 Ω
- 6π Ω

**Q.**The electric field intensity E, current density J and specific resistance k are related to each other through the relation

- E=Jk
- E=Jk
- E=kJ
- k=JE