An electron moves in a straight line inside a charged parallel plate capacitor of uniform charge density σ. The time taken by the electron to cross the parallel plate capacitor undeflected when the plates of the capacitor are kept under constant magnetic field of induction  \((\vec{B})\) is

(a)

\({ \varepsilon }_{ ° }\frac { elB }{ \sigma } \)

(b)

\({ \varepsilon }_{ ° }\frac { lB }{ \sigma {l} } \)

(c)

\({ \varepsilon }_{ ° }\frac { lB }{ {e}\sigma } \)

(d)

\({ \varepsilon }_{ ° }\frac { lB }{ \sigma } \)

A circular coil of radius 5 cm and 50 turns carries a current of 3 ampere. The magnetic dipole moment of the coil is nearly ____.

(a)

1.0 A m²

(b)

1.2 A m²

(c)

0.5 A m²

(d)

0.8 A m²

Three wires of equal lengths are bent in the form of loops. One of the loops is circle, another is a semi-circle and the third one is a square. They are placed in a uniform magnetic field and same electric current is passed through them. Which of the following loop configuration will experience greater torque?

(a)

Circle

(b)

Semi-circle

(c)

Square

(d)

All of them

A wire of length l carrying a current I along the Y direction is kept in a magnetic field is given by \(\vec { B } =\frac { \beta }{ \sqrt { 3 } } =(\hat { i } +\hat { j } +\hat { k } )T.\) The magnitude of Lorentz force acting on the wire is _____.

(a)

\(\sqrt { \frac { 2 }{ { 3 } } } \beta Il\)

(b)

\(\sqrt { \frac { 1 }{ { 3 } } } \beta Il\)

(c)

\(\sqrt { 2 } \beta Il\)

(d)

\(\sqrt { \frac { 1 }{ 2 } } \beta Il\)

A non-conducting charged ring carrying a charge of q, mass m and radius r is rotated about its axis with constant angular speed ω. Find the ratio of its magnetic moment with angular momentum is _____.

(a)

\(\\ \frac { q }{ m } \)

(b)

\(\\ \frac { 2q }{ m } \)

(c)

\(\\ \frac { q }{ 2m } \)

(d)

\(\\ \frac { q }{ 4m } \)