Define Ampere from two current carrying parallel wires.

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) $Image$

$(A)$ If $\vec{B}$ is along $\hat{z}, F \propto(L+R)$

$(B)$ If $\overrightarrow{ B }$ is along $\hat{ x }, F =0$

$(C)$ If $\vec{B}$ is along $\hat{y}, F \propto(L+R)$

$(D)$ If $\overrightarrow{ B }$ is along $\hat{ z }, F =0$

A large current carrying plate is kept along $y-z$ plane with $k$ $amp$ current per unit length in the $+ve$ $y$ direction. Find the net force on the semi cricular current carrying looplying in the $x-y$ plane. Radius of loop is $R$, current is $i$ and centre is at $(d,0, 0)$ where $(d > R)$

The magnetic field existing in a region is given by $\vec{B}=B_0\left(1+\frac{x}{l}\right) \hat{k}$. A square loop of edge I and carrying a current $i$, is placed with its edge parallel to the $x-y$ axes. Find the magnitude of the net magnetic force experienced by the loop

A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

Two parallel wires in free space are $10\, cm$ apart and each carries a current of $10\, A$ in the same direction. The force one wire exerts on the other per metre of length is