A particle of mass $m$ and charge $q$ describes a circular path of radius $R$ in a magnetic field. If its mass and charge were $2 m$ and $\frac{q}{2}$ respectively, the radius of its path would be
Assertion (A): The energy of a charged particle moving in a magnetic field does not change.
Reason (R): It is because the work done by the magnetic force on the charge moving in a magnetic field is zero.
Two long parallel wires kept $$2 \mathrm{~m}$$ apart carry $$3 \mathrm{~A}$$ current each, in the same direction. The force per unit length on one wire due to the other is
Assertion (A): The deflecting torque acting on a current carrying loop is zero when its plane is perpendicular to the direction of magnetic field.
Reason (R): The deflecting torque acting on a loop of magnetic moment $$\vec{m}$$ in a magnetic field $$\vec{B}$$ is given by the dot product of $$\vec{m}$$ and $$\vec{B}$$.
A long straight wire of radius '$$a$$' carries a steady current $$I$$. The current is uniformly distributed across its area of cross-section. The ratio of magnitude of magnetic field $$\vec{B}_1$$ at $$\frac{a}{2}$$ and $$\vec{B}_2$$ at distance $$2 a$$ is
Reason (R) : The magnetic moment of a current carrying loop is directly proportional to the area of the loop.
Derive an expression for magnetic force $\vec{F}$ acting on a straight conductor of length $L$ carrying current I in an external magnetic field $\vec{B}$. Is it valid when the conductor is in zig-zag form? Justify.
An electron moving with a velocity $\vec{v}=\left(1.0 \times 10^7\right.$ $\mathrm{m} / \mathrm{s}) \hat{i}+\left(0.5 \times 10^7 \mathrm{~m} / \mathrm{s}\right) \hat{j}$ enters a region of uniform magnetic field $\vec{B}=(0.5 \mathrm{mT}) \hat{j}$. Find the radius of the circular path described by it. While rotating; does the electron trace a linear path too? If so, calculate the linear distance covered by it during the period of one revolution.
(a) Write the expression for the Lorentz force on a particle of charge $$q$$ moving with a velocity $$\vec{v}$$ in a magnetic field $$\vec{B}$$. When is the magnitude of this force maximum? Show that no work is done by this force on the particle during its motion from a point $$\vec{r_1} \text { to point } \vec{r}_2 \text {. }$$
OR
(b) A long straight wire $$A B$$ carries a current I. A particle (mass $$m$$ and charge $$q$$ ) moves with a velocity $$\vec{v}$$, parallel to the wire, at a distance $$d$$ from it as shown in the figure. Obtain the expression for the force experienced by the particle and mention its directions.
