Magnetic Field Due to Finite Wire

Q.

A current I flows in a long thin walled cylinder of radius R. What pressure do the walls of the cylinder experience?

1. $\frac{{\mu }_{0}I}{8\pi R}$
   

2. $\frac{{\mu }_0{I}^2}{8{\pi }^2{R}^2}$
   

3. $\frac{{\mu }_0{I}^2}{16\pi R^2}$
   

4. $\frac{{\mu }_{0}I}{4{\pi }^{2}R}$
   

Q. An infinite wire placed along z-axis has current $i_1$ in positive z-axis. Another wire PQ placed in x-y plane along y-axis carry current $i_2$ along y-axis wire PQ is at distance a from wire carrying current $i_1$. Net force acting on wire PQ is

1. $\frac{{\mu }_0}{2\pi }{i}_1{i}_{2}2\mu F\left(\frac{2}{\sqrt{3}}\right)$
2. $\frac{{\mu }_0}{2\pi }{i}_1{i}_{2}ln\left(2\right)$
3. $0$
4. $\frac{{\mu }_0}{2\pi }{i}_1{i}_2$

Q. Find the magnetic field due to a current carrying wire at point P. (a =7 cm)

1. $2\times {10}^{-7}$ Tesla
2. $3\times {10}^{-7}$ Tesla
3. ${10}^{-5}$ Tesla
4. $7\times {10}^{-5}$ Tesla

Q. Current i flows through a long conducting wire bent at right angle as shown in figure. The magnetic field at a point P on the right bisector of the angle XOY at a distance r from O is

1. $\frac{{\mu }_{0}i}{\pi r}$
   
2. $\frac{2{\mu }_{0}i}{\pi r}$
   
3. $\frac{{\mu }_{0}i}{4\pi r}(\sqrt{2}+1)$
   
4. $\frac{{\mu }_0}{4\pi }.\frac{2i}{r}(\sqrt{2}+1)$

Q.

For the figure given below, the total magnetic induction at point O (due to curved and straight portion) will be

1. $\frac{{\mu }_{0}i}{2\pi r}$

2. $\frac{{\mu }_{0}i}{2\pi r}(\pi -\varphi +tan\varphi )$

3. $\frac{{\mu }_{0}i}{\pi r}(\pi -\varphi +tan\varphi )$

4. 0

Q. If the magnetic field at ‘P’ can be written as $K$ $\tan \left(\frac{\alpha }{2}\right)$, then $K$ is

1. $\frac{{\mu }_{0}I}{4\pi d}$
2. $\frac{{\mu }_{0}I}{2\pi d}$
3. $\frac{{\mu }_{0}I}{\pi d}$
4. $\frac{2{\mu }_{0}I}{4\pi d}$

Q. Find B - field due to the following system at ‘o’.

1. $Zero$
2. $\frac{{\mu }_{0}i}{2\pi R}tan\theta$
3. $\frac{{\mu }_{0}i}{2\pi R}\theta$
4. $\frac{{\mu }_{0}i}{2\pi R}(\theta -tan\theta )$

Q. Figure shows a square loop ABCD with edge length a. The resistance of the wire ABC is r and that of ADC is 2r. The value of magnetic field at the centre of the loop assuming uniform wire is

1. $\frac{\sqrt{2}{\mu }_{0}i}{3\pi a}\odot$
   
2. $\frac{\sqrt{2}{\mu }_{0}i}{3\pi a}\otimes$
   
3. $\frac{\sqrt{2}{\mu }_{0}i}{\pi a}\odot$
   
4. $\frac{\sqrt{2}{\mu }_{0}i}{\pi a}\otimes$

Q. A finite wire carrying current is placed along the Y axis and carries current in +Y direction. At any random point lying in the XY plane and 1st quadrant of assumed cartesian system, the field will point toward?

1. -Z direction
2. +Y direction
3. -X direction
4. +Z direction