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Q.

A ring of radius  R carries a current  i as shown. It is situated in the yz plane with its center at the origin. The current is clockwise when viewed from the side of positive  x-axis (right to left). An electron is projected with a velocity 3i^+4j^−k^ from the point ‘p’ having coordinates  3R,0,0. What is the force experienced by the electron at this moment, if ‘e’ is the magnitude of charge on electron

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a

μoei16R−j^−4k^

b

μoei16Rj^+4k^

c

μoei4R−j^−4k^

d

μoei32Rj^+4k^

answer is A.

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Detailed Solution

B due to ring at x=3R is B=μ0iR22R2+x23/2B=μ0iR22(R)2+(3R)23/2⇒B=μ0iR22×8R3=μ0i16R, along the negative x− direction ∴B→=-μ0i16Ri^Velocity of the particle isv→=3i^+4j^−k^ Force on the particle isF→=qv→×B→ ⇒F→=-e3i^+4j^−k^×-μoi16Ri^ ⇒F→=μoie16R3i^×i^+4j^×i^+−k^×i^ ⇒F→=μoie16R0−4k^−j^∴F→=μoie16R−j^−4k^
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A ring of radius  R carries a current  i as shown. It is situated in the yz plane with its center at the origin. The current is clockwise when viewed from the side of positive  x-axis (right to left). An electron is projected with a velocity 3i^+4j^−k^ from the point ‘p’ having coordinates  3R,0,0. What is the force experienced by the electron at this moment, if ‘e’ is the magnitude of charge on electron