A wire carrying a current $i$ is placed in a uniform magnetic field in the form of the curve $y = a\sin \,\left( {\frac{{\pi x}}{L}} \right)\,0 \le x \le 2L.$ The force acting on the wire is
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(c) The given portion of the curved wire may be treated as a straight wire of length $2L$ which experiences a magnetic force ${F_m} = Bi(2L)$
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A wire carrying current $I$ and other carrying $2I$ in the same direction produces a magnetic field $B$ at the mid point. What will be the field when $2I$ wire is switched off
For a positively charged particle moving in a $x-y$ plane initially along the $x$-axis, there is a sudden change in its path due to the presence of electric and/or magnetic fields beyond $P$. The curved path is shown in the $x-y$ plane and is found to be non-circular. Which one of the following combinations is possible
The resistance of a galvanometer is $25\, ohm$ and it requires $50\,\mu A$ for full deflection. The value of the shunt resistance required to convert it into an ammeter of $5\, amp$ is
One of the two identical conducing wires of length $L$ is bent in the form of a circular loop and the other one into a circular coil of $N$ identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop $(B_L)$ to that at the centre of the coil $(B_C),$; $.\,\frac {B_L}{B_C}$ will be
An arbitrary shaped closed coil is made of a wire of length $L$ and a current $I$ ampere is flowing in it. If the plane of the coil is perpendicular to magnetic field $\mathop B\limits^ \to $, the force on the coil is
As shown in the figure, two infinitely long, identical wires are bent by $90^o$ and placed in such a way that the segments $LP$ and $QM$ are along the $x-$ axis, while segments $PS$ and $QN$ are parallel to the $y-$ axis. If $OP = OQ = 4\, cm$, and the magnitude of the magnetic field at $O$ is $10^{-4}\, T$, and the two wires carry equal current (see figure), the magnitude of the current in each wire and the direction of the magnetic field at $O$ will be $(\mu_ 0 = 4\pi \times10^{-7}\, NA^{-2})$
In figure shows three long straight wires $P, Q$ and $R$ carrying currents normal to the plane of the paper. All three currents have the same magnitude. Which arrow best shows the direction of the resultant force on the wire $P$