Force Due to Magnetic Fields

Q. A charged particle moves with a uniform velocity $4a_x$ m/s in a region where $\overrightarrow{E}=20a_y$ V/m and The value of $B_0$ such that the velocity of the particlr remains constant is

1. $5$
2. $1$
3. $1.75$
4. $0$

Q. A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction.The magnetic field lines inside the cylinder will

1. bend closer to the cylinder axis
2. bend farther away from the axis.
3. remain uniform as before
4. cease to exist inside the cylinder.

Q. A particle with charge 6 nC is moving in a uniform magnetic field $\overrightarrow{B}=\left(1.23T\right){\hat{a}}_z$ .The magnetic force on a particle is measured to be $\overrightarrow{F}=(4.5\times {10}^7){\hat{a}}_x+(7.5\times {10}^7){\hat{a}}_{y}N$
Select the correct statement(s).

1. The dot product of velocity of particle and magnetic force is zero
2. The component of velocity in y-direction is always zero
3. (c)Magnetic field intensity in air is $9.78\times {10}^{5}A/m$
4. Total force on particle when it is moving in both electric and magnetic field with electric field $\overrightarrow{E}=1{\hat{a}}_z$ volt / m is given as
   $(4.5\times {10}^7{\hat{a}}_x+7.5\times {10}^7{\hat{a}}_{y}N)$

Q. Two long parallel current carrying wires are separated by 5 cm in air and are carrying current of 40A in the opposite direction. The force per meter length between the wires will be .

1. $-6.4\times {10}^{-3}N$
2. $6.4\times {10}^{-3}N$
3. $-3.2\times {10}^{-3}N$
4. $3.2\times {10}^{-3}N$

Q. A conductor is located at x = 0.4 m, y = 0 and 0 < z <2 m, which carries a current of 10 A in $\widehat{a_z}$ direction along the length of conductor, $\overrightarrow{B}=2.5\widehat{a_x}T$ is the magnetic field density. The torque generated about the z-axis will be

1. $20\widehat{a_y}$ N-m
2. $20\widehat{a_x}$N-m
3. $10\widehat{a_y}$ N-m
4. $20\widehat{a_z}$ N-m

Q. If two parallel wires are carrying currents in opposite direction, then force experienced by one conductors due to other will be

1. parallel to wire and attractive
2. perpendicular to wire and attractive
3. parallel to wire and repulsive
4. perpendicular to wire and repulsive

Q. A uniform and constant magnetic field $B=\hat{z}B$ exists in the $\hat{z}$ direction in vacuum. A particle of mass m with a small charge q is introduced into this region with an initial velocity $v=\hat{x}{v}_x+\hat{z}{v}_z$. Given that B, m, q, $v_{x}and{v}_z$ are all non-zero. Which one of the following describes the eventual trajectory of the particle?

1. Helical motion in the $\hat{z}$ direction.
2. Circular motion in the xy plane
3. Linear motion in the $\hat{z}$ direction
4. Linear motion in the $\hat{x}$ direction.

Q. A point charge of 10C moves with a uniform velocity of $2\widehat{a_x}-4\widehat{a_z}m/s$ in electromagnetic field having $\overrightarrow{E}=\widehat{a_x}-3\widehat{a_y}+4\widehat{a_z}V/mand\hat{B}=0.3\widehat{a_x}+0.1\widehat{a_y}Wb/m^2$. The magnitude of force exerted on charge is

1. 61.02 mN
2. 159.70 mN
3. 61.02 N
4. 159.70 N

Q. Consider a straight conductor of length 2m. Carrying a current of 10 A in the +z direction. If the conductor is placed in a field of $\overrightarrow{B}=0.02({\hat{a}}_y-{\hat{a}}_x)Wb/m^2$ , then the force on per unit length of the conductor is

1. $-0.4({\hat{a}}_x+{\hat{a}}_y)N/m$
2. $-0.4({\hat{a}}_x-{\hat{a}}_y)N/m$
3. $-0.2({\hat{a}}_x+{\hat{a}}_y)N/m$
4. $0.2({\hat{a}}_x+{\hat{a}}_y)N/m$

Q. The current diensty in a medium is given by

$\overrightarrow{J}=\frac{400sin\theta }{2\pi (r^2+4)}{\hat{a}}_{r}A{m}^{-2}$

The total current and the average current density flowing through the portion of a spherical surface

r = 0.8 m, $\frac{\pi }{12}\le \theta \le \frac{\pi }{4},0\le 2\pi$ are given, respectively, by

1. 15.09 A, 12.86 $A{m}^{-2}$
2. 7.17 A, 6.88 $A{m}^{-2}$
3. 12.86 A, 9.23 $A{m}^{-2}$
4. 10.28 A, 7.56 $A{m}^{-2}$