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Magnetic Effects of Current and Magnetism

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Q 1. An infinitely long conductor {tex} P Q R {/tex} is bent to form a right angle as shown in diagram. A current {tex} I {/tex} flows through {tex} P Q R {/tex}. The magnetic field due to this current at the point {tex} M {/tex} is {tex} H _ { 1 } {/tex}. Now, another infinitely long straight conductor {tex} Q S {/tex} is connected at {tex} Q {/tex} so that current is {tex} I / 2 {/tex} in {tex} Q R {/tex} as well as in {tex} Q S , {/tex} the current in {tex} P Q {/tex} remaining unchanged. The magnetic field at {tex} M {/tex} is now {tex} H _ { 2 } . {/tex} The ratio {tex} H _ { 1 } / H _ { 2 } {/tex} is given by

{tex} 1 / 2 {/tex}

{tex}1{/tex}

{tex} 2 / 3 {/tex}

{tex}2{/tex}

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Q 2. The magnetic field lines due to a bar magnet are correctly shown in

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Q 3. An electron travelling with a speed u along the positive {tex} x - {/tex} axis enters into a region of magnetic field where {tex} B = - B _ { 0 } \hat { k } {/tex} {tex} ( x /> 0 ) . {/tex} It comes out of the region with speed v then

{tex} v = u {/tex} at {tex} y > 0 {/tex}

{tex} v = u {/tex} at {tex} y < 0 {/tex}

{tex} v > u {/tex} at {tex} y > 0 {/tex}

{tex} v > u {/tex} at {tex} y < 0 {/tex}

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Q 4. A magnetic field {tex} \vec { B } = B _ { 0 } \hat { J } , {/tex} exists in the region a {tex} < x < 2 a {/tex}, and {tex} \bar { B } = - B _ { 0 } \hat { j } , {/tex} in the region {tex} 2 a < x < 3 a {/tex}, where {tex} B _ { 0 } {/tex} is a positive constant. A positive point charge moving with a velocity {tex} \vec { v } = v _ { 0 } \hat { i } , {/tex} where {tex} v _ { 0 } {/tex} is a positive constant, enters the magnetic field at {tex} x = a . {/tex} The trajectory of the charge in this region can be like

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Q 5. An infinitely long hollow conducting cylinder with inner radius {tex} R / 2 {/tex} and outer radius {tex} R {/tex} carries a uniform current density along its length. The magnitude of the magnetic field, {tex} | \vec { B } | {/tex} as a function of the radial distance {tex} r {/tex} from the axis is best represented by

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