Ampere's Circuital Law

Q. Find the net electric field due to a finite wire of linear charge density $+\lambda \text{C/m}$ at a point $\text{P}$ located at a perpendicular distance $d$ as shown in the figure.

$[K=\frac{1}{4\pi {\epsilon }_0}]$

1. $2\sqrt{2}\frac{K\lambda }{d}$
2. $\frac{1}{2\sqrt{2}}\frac{K\lambda }{d}$
3. $\sqrt{2}\frac{K\lambda }{d}$
4. $\frac{K\lambda }{\sqrt{2}d}$

Q. A charge $+q$ is fixed at each of the point $x=x_0,x=3x_0,x=5x_0...$ upto infinity and a charge $-q$ fixed at each of the points $x=2x_0,x=4x_0,x=6x_0...$ upto infinity. Here $x_0$ is a positive constant. The potential at the origin due to this system of charges is

1. Infinity
2. Zero
3. $\frac{q}{4\pi {\epsilon }_0{x}_0{\log }_{e\left(2\right)}}$
4. $\frac{q{\log }_e\left(2\right)}{4\pi {\epsilon }_0{x}_0}$

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

Q. A cylindrical conductor of radius $R$ is carrying a constant current $i$. The plot of the magnitude of the magnetic field $B$ with distance $d$ from the centre of the conductor is correctly represented by the figure

1. 
2. 
3. 
4. 

Q. Initially the spheres $\text{A}$ and $\text{B}$ are at potential $V_A$ and $V_B$. The potential of sphere $\text{A}$ when sphere $\text{B}$ is earthed is

1. $V_A-V_B$
2. $V_B-V_A$
3. $V_A$
4. $V_A+V_B$

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

Q. ABCDA is an amperian loop, $\oint \overrightarrow{B}.\overrightarrow{dl}$ along the loop is

1. $56\pi \times {10}^{-7}$
2. zero
3. $28\pi \times {10}^{-7}$
4. $11\pi \times {10}^{-7}$

Q. A cylindrical cavity of diameter $a$ exists inside a cylinder of diameter $2a$ as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density $J$ flows along the length. If the magnitude of the magnetic field at the point $P$ is given by $\frac{N}{12}{\mu }_{0}aJ$, then the value of $N$ is

Q. The magnetic field at the centre of a uniform charged ring (Q) of radius $R$ rotating at angular velocity $\omega$ about an axis passing through a diameter is $\frac{{\mu }_0}{4\pi }\frac{nQ\omega }{R}$, then n is

Q. For loop $ABCDA$, $\oint \overrightarrow{B}.\overrightarrow{di}$ will be?

1. equals to $4{\mu }_0$
2. greater than $4{\mu }_0$
3. less than $4{\mu }_0$
4. None of the above