Magnetic Effects of Current

In which case will the particle move in a straight line with constant velocity?

In which case will the particle describe a helical path with axis along the positive $z$ direction?

In which case would the particle move in a straight line along the negative direction of $y$-axis (i.e., move along $-\hat{y}$)?

A symmetric star shaped conducting wire loop is carrying a steady state current $I$ as shown in the figure. The distance between the diametrically opposite vertices of the star is $4a$. The magnitude of the magnetic field at the center of the loop is

A uniform magnetic field $B$ exists in the region between $x = 0$ and $x = \frac{3R}{2}$ (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge $+Q$ and momentum $p$ directed along $x$-axis enters region 2 from region 1 at point $P_1$ $(y = -R)$. Which of the following option(s) is/are correct?

When a current of 5 mA is passed through a galvanometer having a coil of resistance 15 Ω, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 − 10 V is :

In a certain region static electric and magnetic fields exist. The magnetic field is given by $\vec B=B_0\left(\hat i+2\hat j-4\hat k\right)$. If a test charge moving with a velocity $\vec v=v_0\left(3\hat i-\hat j+2\hat k\right)$ experiences no force in that region, then the electric field in the region, in SI units, is :

A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current $I=I_o\cos(\omega t)$. The emf induced in the smaller inner loop is nearly :

According to Bohr's theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the n$^{\text{th}}$ orbit is proportional to : (n = principal quantum number)

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :

A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop (abcd) of sides 10 cm × 5 cm carries a current I of 12 A. Out of the following different orientations which one corresponds to stable equilibrium ?

A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90° vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of $10\ \mathrm{A\,s^{-1}}$. Which of the following statement(s) is(are) true?

Consider two identical galvanometers and two identical resistors with resistance $R$. If the internal resistance of the galvanometers $R_C<R/2$, which of the following statement(s) about any one of the galvanometers is(are) true?

Two identical wires A and B, each of length '$l$', carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side '$a$'. If $B_A$ and $B_B$ are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\dfrac{B_A}{B_B}$ is :

A galvanometer having a coil resistance of 100 Ω gives a full scale deflection, when a current of 1 mA is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10 A, is :

A 50 Ω resistance is connected to a battery of 5 V. A galvanometer of resistance 100 Ω is to be used as an ammeter to measure current through the resistance, for this a resistance $r_s$ is connected to the galvanometer. Which of the following connections should be employed if the measured current is within 1% of the current without the ammeter in the circuit ?

A galvanometer has a 50 division scale. Battery has no internal resistance. It is found that there is deflection of 40 divisions when R = 2400 Ω. Deflection becomes 20 divisions when resistance taken from resistance box is 4900 Ω. Then we can conclude :

A conductor (shown in the figure) carrying constant current $I$ is kept in the $x$-$y$ plane in a uniform magnetic field $\vec B$. If $F$ is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is(are)

Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are $w_1$ and $w_2$ and thicknesses are $d_1$ and $d_2$, respectively. Two points $K$ and $M$ are symmetrically located on the opposite faces parallel to the $x$-$y$ plane (see figure). $V_1$ and $V_2$ are the potential differences between $K$ and $M$ in strips 1 and 2, respectively. Then, for a given current $I$ flowing through them in a given magnetic field strength $B$, the correct statement(s) is(are)

Consider two different metallic strips (1 and 2) of same dimensions (length $l$, width $w$ and thickness $d$) with carrier densities $n_1$ and $n_2$, respectively. Strip 1 is placed in magnetic field $B_1$ and strip 2 is placed in magnetic field $B_2$, both along positive $y$-directions. Then $V_1$ and $V_2$ are the potential differences developed between $K$ and $M$ in strips 1 and 2, respectively. Assuming that the current $I$ is the same for both the strips, the correct option(s) is(are)