Current Density Vector

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

1. 18 : 1
2. 9 : 1
3. 6 : 1
4. 2 : 3

Q. The current density across a cylindrical conductor of radius $R$ varies in magnitude according to the equation $J=J_0(1-\frac{r}{R})$ where $r$ is the distance from the central axis. Thus, the current density is maximum $J_0$ at the axis ($r=0$) and decreases linearly to zero at the surface $(r=R)$. The current in terms of $J_0$ and conductor's cross-sectional area $A$ is :-

1. $\frac{J_{0}A}{3}$
2. $\frac{J_{0}A}{6}$
3. $\frac{J_{0}A}{2}$
4. $\frac{J_{0}A}{5}$

Q. A wire is placed along a parabola $y=4x^2$ from x =-1 to x = +1 with a current of 10 A flowing through it and a uniform cross-sectional area of $0.1m^2$. What is the direction and magnitude of the current density vector of this wire?

1. $100A/m^2$ in the positive x direction
2. $100A/m^2$ in the negative x direction
3. $1A/m^2$ in the positive y direction
4. $100A/m^2$ at every cross-section with its direction tangential to the wire in the direction of current.

Q. An electric current of 8 Amperes is measured across an area of $50c{m}^2$, then current density in this area is:

1. Must be $1600A/m^2$
2. Must be greater than or equal to $1600A/m^2$
3. Must be less than or equal to $1600A/m^2$
4. Cannot say

Q. An electric current flows along conductor AB as shown in figure.

$\overrightarrow{E}$ in conductor AB varies as

1. 
2. 
3. 
4. 

Q. An electric current of 8 Amperes is measured across an area of $50c{m}^2$, then current density in this area is:

1. Must be $1600A/m^2$
2. Must be greater than or equal to $1600A/m^2$
3. Must be less than or equal to $1600A/m^2$
4. Cannot say

Q. I apply an electric field of ${10}^{5}N/C$ on a conductor of cross section $4m{m}^2$ 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?

1. $3\times {10}^{4}N/C$
2. $5\times {10}^{4}N/C$
3. $4\times {10}^{4}N/C$
4. $2\times {10}^{4}N/C$

Q. I apply an electric field of ${10}^{5}N/C$ on a conductor of cross section $4m{m}^2$ 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?

1. $3\times {10}^{4}N/C$
2. $5\times {10}^{4}N/C$
3. $4\times {10}^{4}N/C$
4. $2\times {10}^{4}N/C$

Q. The current density across a cylindrical conductor of radius $R$ varies in magnitude according to the equation $J=J_0(1-\frac{r}{R})$ where $r$ is the distance from the central axis. Thus, the current density is maximum $J_0$ at the axis ($r=0$) and decreases linearly to zero at the surface $(r=R)$. The current in terms of $J_0$ and conductor's cross-sectional area $A$ is :-

1. $\frac{J_{0}A}{3}$
2. $\frac{J_{0}A}{6}$
3. $\frac{J_{0}A}{2}$
4. $\frac{J_{0}A}{5}$