Protons and ∝-particles of equal momenta enter a uniform magnetic field normally. The radii of their orbits will have the ratio.

Solution

A square coil of side a carries a current I. The magnetic field at the centre of the coil is

\(\frac{\mu _{0}I}{a\pi }\)
\(\frac{\sqrt{2}\mu _{0}I}{a\pi }\)
\(\frac{\mu _{0}I}{\sqrt{2}a\pi }\)
\(\frac{2\sqrt{2}\mu _{0}I}{2\pi }\)

Solution

Two particles X and Y having equal charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii R₁ and R₂ respectively. The ratio of the mass of X to that of Y is

\(\sqrt{\frac{R_{1}}{R_{2}}}\)
\(\sqrt{\frac{R_{1}}{R_{2}}}\)
\(\left ( \frac{R_{1}}{R_{2}} \right )^{2}\)
\(\sqrt{\frac{R_{2}}{R_{1}}}\)

Solution

A current of I ampere flows along an infinitely long straight thin walled hollow metallic cylinder of radius r. The magnetic field at any point inside the cylinder at a distance x from the axis of the cylinder is

∞
\(\frac{\mu _{0}I}{2\pi r}\)
\(\frac{\mu _{0}I}{2\pi x}\)
zero

Solution

Since no current is enclosed inside the hollow conductor. Hence B_inside= 0.

A uniform electric field and a uniform magnetic field exist in a region in the same direction. An electron is projected with velocity pointed in the same direction. The electron will

turn to its right
turn to its left
keep moving in the same direction but its speed will increase
keep moving in the same direction but its speed will decrease

Solution

No magnetic force acts on the electron and force due to electric field will act opposite to its initial direction of motion. Hence its velocity decreases in magnitude.

A current of I ampere flows in a wire forming a circular are of radius r metres subtending an angle θ at the centre as shown.The magnetic field at the centre O in tesla is

\(\frac{\mu _{0}I\theta }{4\pi r}\)
\(\frac{\mu _{0}I\theta }{2\pi r}\)
\(\frac{\mu _{0}I\theta }{2 r}\)
\(\frac{\mu _{0}I\theta }{4r}\)

Solution

The magnetic flux density B at a distance r from a long straight wire carrying a steady current varies with r as

If we double the radius of a coil keeping the current throughit unchanged, then the magnetic field at any point at a large distance from the centre becomes approximately

double
three times
four times
one-fourth

Solution

If an electron and a proton having same momenta enter perpendicular to a magnetic field, then

curved path of electron and proton will be same(ignoring the sense of revolution)
they will move undeflected
curved path of electron is more curved than that of the proton
path of proton is more curved

Solution

r = mv/Bq is same for both.

If in a circular coil A of radius R, current I is flowing and in another coil B of radius 2R a current 2I is flowing, then the ratio of the magnetic fields BA and BB, produced by the m will be

Solution

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