Equal currents are flowing in three infinitely long wires along positive x, y and z directions. The magnetic field at …..

Q. Equal currents are flowing in three infinitely long wires along positive x, y and z directions. The magnetic field at a point (0, 0, -a) would be (i = current in each wire )

(a) $\displaystyle \frac{\mu_0 i}{2\pi a} (\hat{j}-\hat{i})$

(b) $\displaystyle \frac{\mu_0 i}{2\pi a} (\hat{i}-\hat{j})$

(c) $\displaystyle \frac{\mu_0 i}{2\pi a} (\hat{j}+\hat{i})$

(d) $\displaystyle \frac{\mu_0 i}{2\pi a} (-\hat{i}-\hat{j})$

Ans: (a)

A tightly-wound long solenoid has n turns per unit length, radius r and carries a current i. A particle having …..

Q. A tightly-wound long solenoid has n turns per unit length, radius r and carries a current i. A particle having charge q and mass m is projected from a point on the axis in the direction perpendicular to the axis. The maximum speed for which particle does not strike the solenoid will be

(a) $\displaystyle \frac {\mu_0 q r n i}{2m}$

(b) $\displaystyle \frac {\mu_0 q r n i}{m}$

(c) $\displaystyle \frac {2\mu_0 q r n i}{3m}$

(d) None of these

Ans: (a)

Sol: Magnetic field inside the solenoid is B = μ0 n i , along the axis of solenoid

Since velocity is Perpendicular to B , hence particle moves in a circle of radius

$\displaystyle R = \frac{m v}{q B} = \frac{m v}{q \mu_0 n i}$

If particle does not strike solenoid

R ≤ r/2

$\displaystyle \frac{m v}{q \mu_0 n i} \le \frac{r}{2}$

$\displaystyle v \le \frac{\mu_0 n i q r}{2 m}$

$\displaystyle v_{max} = \frac{\mu_0 n i q r}{2 m}$

An equilateral triangle frame PQR of mass M and side a is kept under the influence of magnetic force due to…..

Q. An equilateral triangle frame PQR of mass M and side a is kept under the influence of magnetic force due to inward perpendicular magnetic field B and gravitational field as shown in the figure. The magnitude and direction of current in the frame so that the frame remains at rest is

(a) $\displaystyle I = \frac{2Mg}{aB}$ , anticlockwise

(b) $\displaystyle I = \frac{2Mg}{aB}$ , clockwise

(c) $\displaystyle I= \frac{Mg}{aB}$ , anticlockwise

(d) $\displaystyle I= \frac{Mg}{aB}$ , clockwise

Ans: (b)

A wire carrying a current of 3A is bent in the form of a parabola y2 = 4-x as shown in figure …..

Q. A wire carrying a current of 3A is bent in the form of a parabola y2 = 4-x as shown in figure, where x and y are in metre. The wire is placed in a uniform magnetic field $\displaystyle \vec{B} = 5 \hat{k}$ tesla . The force acting on the wire is

(a) $\displaystyle 60 \hat{i} N$

(b) $\displaystyle -60 \hat{i} N$

(c) $\displaystyle 30 \hat{i} N$

(d) $\displaystyle -30 \hat{i} N$

Ans: (a)

Sol: y2 = 4 – x

At x =0 , y = ± 2

$\displaystyle \vec{L} = 4 \hat{j}$

(As , force on parabola is same as force on  wire of length L )

$\displaystyle \vec{F} = i (\vec{L} \times \vec{B})$

$\displaystyle \vec{F} = 3 (4 \hat{j} \times 5 \hat{k})$

$\displaystyle \vec{F} = 60 \hat{i}$

In the figure shown, a charge q moving with a velocity v along the x-axis enter into a region of uniform magnetic field….

Q. In the figure shown, a charge q moving with a velocity v along the x-axis enter into a region of uniform magnetic field. The minimum value of v so that the charge q is able to enter the region x > b

(a) $\displaystyle \frac{q B b}{m}$

(b) $\displaystyle \frac{q B a}{m}$

(c) $\displaystyle \frac{q B( b -a )}{m}$

(d) $\displaystyle \frac{q B( b +a )}{2m}$

Ans: (c)