A force of \(10 \; N\) acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be ...... \(N\)

The formula \(X = 5YZ^2\),  \(X\) and \(Z\) have dimensions of capacitance and magnetic field respectively. What are the dimensions of \(Y\) in \(SI\) units?

A capacitor has capacitance \(5 \mu F\) when it's parallel plates are separated by air medium of thickness \(d\). A slab of material of dielectric constant \(1.5\) having area equal to that of plates but thickness \(\frac{ d }{2}\) is inserted between the plates. Capacitance of the capacitor in the presence of slab will be \(..........\mu F\)

A solid sphere of mass \(M\) and radius \(R\) is divided into two unequal parts. The smaller part having mass \(M/8\) is converted into a sphere of radius \(r\) and the larger part is converted into a circular disc of thickness \(t\) and radius \(2R\). If \(I_1\) is moment of inertia of a sphere having radius \(r\) about an axis through its centre and \(I_2\) is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia \(I_2/I_1 = \) _____.

The equivalent capacitance between points \(A\) and \(B\) in below shown figure will be..........\(\mu F\).

A uniform rod \(AB\) is suspended from a point \(X\), at a variable distance from \(x\) from \(A\), as shown. To make the rod horizontal, a mass \(m\) is suspended from its end \(A\). A set of \((m, x)\) values is recorded. The appropriate variable that give a straight line, when plotted, are

As shown in the figure, a current of \(2\,A\) flowing in an equilateral triangle of side \(4 \sqrt{3}\,cm\). The magnetic field at the centroid \(O\) of the triangle is: (Neglect the effect of earth's magnetic field.)

An electromagnetic wave travelling in \(x\)-direction is described by field equation \(E_y = 300\sin\omega\left(t - \dfrac{x}{c}\right)\). If the electron is restricted to move in \(y\)-direction only with speed of \(1.5 \times 10^6\) m/s then ratio of maximum electric and magnetic forces acting on the electron is _______.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason(R).
Assertion (A) : Magnetic monopoles do not exist.
Reason (R) : Magnetic field lines are continuous and form closed loops.
In the light of the above statements, choose the most appropriate answer from the options given below :

Proton with kinetic energy of \(1\;MeV\) moves from south to north. It gets an acceleration of \(10^{12}\; \mathrm{m} / \mathrm{s}^{2}\) by an applied magnetic field (west to east). The value of magnetic field :.......\(mT\) (Rest mass of proton is \(1.6 \times 10^{-27} \;\mathrm{kg}\) )

A force \(\mathrm{F}=\alpha+\beta \mathrm{x}^2\) acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant \(\alpha=1 \mathrm{~N}\) then \(\beta\) will be ________.