Ampere's Circuital Law

Q. Magnetic induction at the centre of a current carrying circular coil of radius 15 cm is 5/5 times the magnetic induction at a point on its axis. Distance of this point from the centre of the coil is ?

Q. Does the strength of magnetic field of a straight current carrying conductor depend on its dimensions like length or area of cross section or thickness ?

Q. The particle $P$ shown in figure has a mass of $10\text{mg}$ and a charge of $-0.01\mu \text{C}$. Each plate has a surface area $100{\text{cm}}^2$ on one side. What potential differences $V$ should be applied to the combination to hold $P$ in equilibrium ?

1. $95\text{V}$
2. $43\text{V}$
3. $70\text{V}$
4. $80\text{V}$

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

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. . The dimensional formula of magnetic flux is(a) \lbrack MoL PTA-2\rbrack(c) \lbrack ML2T9A"\rbrack(b) MLOT A2\rbrack2 A-1(d) \lbrack ML2T-1A"\rbrack

Q. If a proton enters a region of uniform magnetic field with velocity $v$ in a direction perpendicular to the magnetic field, then the time period of revolution is $T$. If proton enters with velocity $2v$, the time period will be

1. $2T$
2. $3T$
3. $4T$
4. $T$

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 dimension of magnetic field in M, L, T and C (coulomb) is given as
(1) MT²C^–2 (2) MT^–1C^–1 (3) MT^–2C^–1 (4) MLT^–1C^–1

Q. Consider a metal ring kept on a horizontal plane. A bar magnet is held above the ring with its length along the axis of the ring. If the magnet is dropped freely, the acceleration of the falling magnet is:
$(g$ is acceleration due to gravity)

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. 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 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.