Ampere's Circuital Law

Q.

Sometimes we show an idealised magnetic field which is uniform in a given region and falls to zero abruptly. One such field is represented in figure (35-E12). Using Ampere's law over the path PQRS, show that such a field is not possible.

Q. A long cylindrical conductor of radius $R$ carries current such that current density $J\left(r\right)$ varies with distance $‘r^{\prime }$ from central axis of cylinder. If magnetic field at a distance $r(r<R)$ from axis is $B\left(r\right)=2r^3$. Then current density $J\left(r\right)$ will be given as

1. $J\left(r\right)=\frac{2r^2}{{\mu }_0}$
2. $J\left(r\right)=\frac{8r^2}{{\mu }_0}$
3. $J\left(r\right)=\frac{r^2}{{\mu }_0}$
4. $J\left(r\right)=\frac{4r^2}{{\mu }_0}$

Q. An infinitely long hollow conducting cylinder with radius $R$ carries a uniform current along its surface. Choose the correct representation of magnetic field $\left(B\right)$ as a function of radial distance $\left(r\right)$ from the axis of cylinder.

1. 
2. 
3. 
4. 

Q. A current is flowing through a thin cylindrical shell of radius R. If energy density in the medium, due to magnetic field, at a distance r from axis of the shell is equal to U then which of the following graphs is correct

1. a
2. b
3. c
4. d

Q. A current of $\frac{1}{4\pi }$ amp is flowing in a long straight conductor. The line integral of magnetic induction around a closed path enclosing the current carrying conductor is

1. $16{\pi }^2\times {10}^{-7}wb/m$
2. ${10}^{-7}wb/m$
3. $Zero$
4. $4\pi \times {10}^{-7}wb/m$

Q.

The magnetic field due to a straight conductor of uniform cross section of radius a and carrying a steady current is represented by

1. 
   

2. 
   

3. 
   

4. 
   

Q.

A long thin hollow metallic cylinder of radius 'R' has a current i ampere. The magnetic induction 'B'-away from the axis at a distance r from the axis varies as shown in

1. 

2. 

Q. Find B - field at the centre of a spiral of N - Turns carrying a current i and having inner and outer radii a and b respectively.

1. $\frac{{\mu }_{0}Ni}{2b}$
2. $\frac{{\mu }_{0}Ni}{2(b-a)}ln\left(\frac{b}{a}\right)$
3. $\frac{{\mu }_{0}Ni}{2(b-a)}$
4. $\frac{{\mu }_{0}Ni}{b-a}$

Q. Two thin long parallel wires separated by a distance b are carrying a current i amp each. The magnitude of the force per unit length exerted by one wire on the other is

1. 
2. 
3. 
4. 

Q. in electrostatics is analogous to in magnetostatics.

1. Biot savart law
2. Gauss law
3. Ampere's law
4. Maxwell law