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A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2$a from axis of the wire is:
Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper, as shown. The variation of the magnetic field $B$ along the line $XX’$ is given by
A steady current $i$ flows in a small square loop of wire of side $L$ in a horizontal plane. The loop is now folded about its middle such that half of it lies in a vertical plane. Let $\overrightarrow {{\mu _1}} $ and $\overrightarrow {{\mu _2}} $ respectively denote the magnetic moments due to the current loop before and after folding. Then
A galvanometer having a coil resistance $100 \;\Omega$ gives a full scale deflection when a current of $1 \;\mathrm{mA}$ is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter giving full scale deflection for a potential difference of $10\; \mathrm{V} ?$......$k\Omega$
A particle is moving with velocity $\overrightarrow{ v }=\hat{ i }+3 \hat{ j }$ and it produces an electric field at a point given by $\overrightarrow{ E }=2 \hat{ k }$. It will produce magnetic field at that point equal to (all quantities are in SI units)
An electron moves with a speed of $2 \times 10^5\, m/s$ along the $+ x$ direction in a magnetic field $\vec B = \left( {\hat i - 4\hat j - 3\hat k} \right)\,tesla$. The magnitude of the force (in newton) experienced by the electron is (the charge on electron $= 1.6 \times 10^{-19}\, C$)
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 $(\mu_ 0 = 4\pi \times10^{-7}\, NA^{-2})$
A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let $r_{d}$ and $r_{\alpha}$ be their respective radii of circular path. The value of $\frac{r_{d}}{r_{\alpha}}$ is equal to